Should this abbreviated question use "lose" or "lost?"

Either could be correct; it simply depends on how you reconstruct the full sentence from the headline:

Did you lose some reputation points?

Have you lost some reputation points?

Since English telegraphic style allows both "Did you..." and "Have you..." to be omitted, neither is incorrect, and some readers might balk at either one.

The first one is more ambiguous and can support multiple "timeframe" references.

(Did you) lose some reputation points? - past
(Would you like to) lose some reputation points? - future

Whereas the latter implies something that has happened

(Have you) lost some reputation points?

The ambiguity of the first form leans towards choosing the latter form for clarity.

I'm going on shades of meaning here, but to my ear, "(did you) lose some reputation points?" has an underlying connotation that you took some action that, directly or not, caused the loss of points. "(Have you) lost some reputation points?" has no such implication of agency; something happened, maybe as a result of your action but also maybe because of something entirely out of your control, and now the points cannot be located.

So in addition to the ambiguity that Richard cites in his answer, I prefer the "lost" formation for its closer (in my opinion) approximation to the actual truth, which is that the system did something that made your reputation vanish, not you.