Game shown as loss when there was not mating material

 Then he could have promoted it, and won.

 It is impractical for chess.com to implement the "insufficient losing chances" rule.  The options are:  1.  Ignore the rule, or  2.  Incorporate it into their "insufficient material" rule.  Choosing either of these is a compromise.

Yes, there are compromises in chess.  The rules of the game were arrived at by compromise and are sometimes inconsistent (Take a look at the differences between USCF and FIDE rules - different people had different ideas on how to play the game).

Black (with white's help) could mate in 4

Something that gets lost is that we are playing under chess.com rules.  The current rule on "insufficient material" was developed when members wanted the list of drawn conditions to be expanded to encompass positions where checkmate, although possible, was unlikely.  If you disagree with the policy, petition chess.com to change their rule.

Reminds me of this incident from the 2008 Women's World Championship: http://www.chessbase.com/newsdetail.asp?newsid=4893 (scroll about halfway down).

That one is interesting as the arbiter ruled a draw because checkmate could not be forced, but the rule only requires checkmate by any series of legal moves.  Humans don't always get things right.

He probably confused the requirements of 10.2a, which apply before the flag falls, with the requirements of 6.9, which apply after the flag falls.

 That is a good point.

Woton, you said "There is another rule, "insufficient losing chances" (USCF wording)." I think this not just USCF wording, but also only a USCF rule. I'm pretty sure it's not a FIDE rule. Of course, that doesn't mean that chess.com can't enforce it. But, like I said, what they are enforcing now seems pretty silly. In the K+p vs.K+N situation, white can't lose on time, unless he finds the time to promote to a knight first.

I wonder, what positions exactly qualify as "insufficient losing chances", both under USCF and chess.com rules. (I remember once trying to look up the USCF rules. It appeared that the only way to view them was to mail order them in book form. Talk about obscurantism.)

FIDE 10.2a and the USCF "insufficient losing chances" rule (14H) are similar.  Both require a player to make a claim before the flag falls, and to have an arbiter ajudicate the game (probably by determining if there is a forced checkmate).  The USCF rule is only applicable when a clock without a time delay is being used, so the USCF rule allows the substitution of a clock with a time delay (preferred method) in lieu of adjudication.

I believe that chess.com just sets up certain conditions, like K+R vs. K+R, etc. (either player can checkmate, but it's an easy draw) when determining drawn positions that would fall under "insufficient losing chances".

Note:  You're right about the USCF.  While FIDE rules are available on their web site, the USCF makes you buy the rulebook.

Oh, ok, you're referring to draw claims. That doesn't apply in the case of flag falls. It is therefore, strictly speaking, irrelevant to the discussion. If the flag has fallen, it is to late to claim and considerations of "insufficient losing chances" no longer apply. That is, in both cases #41 and #46, if whites flag fell, he would lose under Fide (and, if I understand you correctly, USCF) rules.

Of course, in the chess.com case it is slightly different, as there are no arbiters to make a claim. However, a more natural solution would seem to be to have the draw offer button change to a draw claim button, just like in the case of move repetitions.

Finally, the question still remains: what positions does chess.com consider without losing chances? it is strange that the p vs N case is drawn, but the N vs N case is not.

You're correct, #41 and #46 are wins after the flag falls.  The problem is that chess.com presently has no way to claim a draw before the flag falls, and, there is no arbiter available.  A solution would be to incorporate a claim draw button and have arbiters available.  That's probably not a cost effective solution to the problem.

(As an aside, on the USCF rulebook case, it is truly absurd that an essential part of tournament conditions isn't even freely available to the participants. I'm not a lawyer, but I'm pretty sure that paid participation in a tournament amounts to entering into a contract and that contracts of which the conditions are not disclosed to all its parties are invalid. 

I'd like to see some American player take this to its extremes: enter into a tournament and play on your first move the brilliant 1.Bc1-e6+Qd1xf7# (that is take with one hand the bishop on c1, with the other the queen and place them on e6 and f7 respectively to administer mate.) Then when an arbiter objects tell him that this is your understanding of the rules and that there is no tournament condition to the opposite effect. Take it to court to get your hard earned prize.)

I agree that hiring arbiters would be silly. However, in the present solution as much as in my proposal (the claim button) it is necessary to specify in advance what positions will be considered of "insufficient losing chances". That is not an argument to make the claim automatic (i.e. to declare situations like #46 drawn upon flag fall).

And, still, the present specification of "insufficient losing chances" is silly, compare the resolution of #46 and #41.

You would not win your case. Everyone seems to have this idea that the American justice system is full of judges saying "Well, your claim is absurd but the letter of the law says you win, so I'll do it." Laws are more vague and judges much more discerning than that.

@mathijs

Since you have to claim a draw for the 3rd repetition and 50 move rules, it makes sense to have to claim a draw under 10.2a.  You might offer that as a suggestion for improvement.

I wouldn't expect to win it, of course. It's just an illustration. I like to take logical fallacies to their extremes, that has nothing to do with my contempt for the American judicial system, but with my mathematical proclivities.

I do think there is a very real problem with the USCF policy under consideration. Take a simple example: if a player, unaware of the rules in this regard, touches a piece, let's go and then moves another piece. He would be forced to take back his move and make one with the touched piece, i.e. he would be forced to abide by a rule that he would have to pay for to know. It is easy to imagine such a case (or something similar) occurring in a situation where prizes are at stake. 

There have been several threads on this topic.  The following link provides some insight into the present chess.com policy.

http://www.chess.com/forum/view/help-support/no-mating-material--draw?page=1

Just go by material. If time runs out, did the other side have sufficient mating material? This is not a slow tournament game.