According to the post on Reddit, “I was not only unable to to access the PSN store to download my games but I’m also now have an issue where my Vita won’t go to “sleep mode” I can tell this because the green light is on and my batter [sic] keeps draining even though I have not been using my Vita. (I’ve tried turning it on and off again with no avail).”
Like we said, the folks at Kotaku have confirmed the problem as well, with their PS Vita being stuck saying “Please wait” for 10 minutes while trying to connect to the PlayStation Store. This seems to affect PS Vita owners who have updated to version 3.57. Sony has yet to comment on the problem, but hopefully they will be able to address it quickly.
In the meantime if you have yet to update your PS Vita, it does seem like it would be a good idea to hold off on updating, at least for now until Sony has issued a fix for it.