Hello,
I am experiencing the same issue regarding twitter feed, and did a little digging.
I’ve discovered that the issue is not with the theme, but with how Twitter deals with it’e request.
Twitter has a limit of 150 request per hour for an IP address. Since I am on a shared hosting service using the same IP with other people, that 150 limit gets used up pretty quickly. I assume the OP is also on a shared hosting server.
more info can be found on the following URL
https://dev.twitter.com/docs/rate-limiting
Chris.