It sounds like "An error occurred while accessing IsolatedStorage". But there's no such exceptions is msdn: http://msdn.microsoft.com/en-us/library/system.io.isolatedstorage.isolatedstoragefile.getlastaccesstime(v=vs.110).aspx
I assume, it can be because i'm calling it inside of Task.Factory.StartNew(). Can it be a reason? It works on wp8 fine.
EDIT:
The problem was that I used GetLastAccessTime(cacheFileName).Millisecond;
As it is said by the link by Agat, miliseconds are always 0 at the wp7. Or, actually, they are even not available, because exception is throwing while trying to access them. So just dont use Milliseconds, and that's it.