Though it never happens please share the screen shot here I will report it to the developers of Chess.com .I would suggest that you should use the normal version of chess.com as the beta version is for testing purposes, though it does not affect the problem you faced but I will tell the developers to see to it.
Thanks for using chess.com.
@bhuchoA I did contact support regarding this issue already. I thought it would be helpful to post in the forums in case anyone else has encountered the same problem.
Similar to my other post you commented on, I also created a duplicate post of this problem in the Chess.com Beta club. The link is below if you would like to read the response I received from support staff and my response, etc.
https://www.chess.com/clubs/forum/view/solo-chess-record-of-games-not-saving
Contact on the link below: : https://support.chess.com/customer/portal/emails/new
If you have already done that and still no profit then only
contact him
https://www.chess.com/member/andreamorandini
or him
https://www.chess.com/member/erik
or him
https://www.chess.com/member/jdcannon
ask them as doubt please don't give them any suggestions.
@bhuchoA I received a reply from @jdcannon from a post I created in the Chess.com Beta group. Thank you for suggesting a few staff to talk to about my question. This is helpful for future reference! 
Link below for reference:
https://www.chess.com/clubs/forum/view/solo-chess-record-of-games-not-saving
" So I heard back on solo chess and at this time we are intentionally not saving progress on solo chess which is a bit weird to me. I will check to see if we have plans to start saving it. "
I tried the Solo Challenge this morning for the first time, at which time I completed all 10 levels. I also tried Level 1 multiple times in a row to try and set a new "record". Once playing a few moves of Level 1, I then left the chess.com site and went back on to see if the record would appear upon my next visit. I was disappointed to see my none of my previous games saved.
This makes it challenging because if it does not retain my previous score, it seems like a waste of time continuing to play that specific feature, as my results will not be logged for future reference.
I have “Beta Chess” mode enabled and tried Solo Chess with two different Internet browsers (Opera and Firefox) and the record of games still did not save. Maybe I'm just mistaken, but I thought that the previous game's record would save so you could come back at a later date and try to surpass your old "score". But maybe I'm incorrect? Just seems odd that you would play 10 Levels of Solo Chess Challenge just to have no record of ever playing it?
For informational purposes, my computer specifications are below.