I've had this happen to me several times. It used to frustrate me as a basic member because the server counts that as one of your 3 problems/day. However, as a premium member, the points you lose get evened out if you keep playing the game.
Tactics Trainer - Skipped Problems

One thing I have noticed is that when you answer a problem wrong you usually lose around 40 points, but if a problem is counted as skipped you usually lose quite a bit more.

Here is what it usually looks like when the problem occurs:
You can play the first move, and no matter whether you get it right or wrong, nothing really happens. Later on a skipped problem will show up in your results. It doesn't show up immediately. The easiest way to tell when it shows up is you answer a problem correctly, get points added to your rating, and your rating is lower than when you started the problem.
Is there any chance that the tactics trainer will be modified to better detect when a problem is skipped versus the javascript not working or there being a network hiccup? I've had at least a dozen problems where either the problem doesn't show up in the window, or it doesn't register anything after I make a move, that end up getting counted as skipped after I close the window because nothing has happened for a couple of minutes. It doesn't seem to be a network problem on my end as I am able to go to different sites with my browser. I have run into this problem with both Internet Explorer and Firefox.
It is just annoying to lose points when you don't get the opportunity to answer the problem.