How long are domain policies cached on the client?

I've set it up so that our branch (about 10 miles away) can connect to the main office via a VPN connection and has successfully connected to the main office's domain, logged in as a user and picked up the associated Group Policy (GPO). The GPO for that account at the Branch may change once or twice a year at most. Since I have no use for the VPN until a policy change is made, do I have to worry about the locally cached domain account and associated GPO expiring anytime soon and denying the user the ability to log in?

The GPO won't expire any sooner from a cache because it will still have to authenticate on the server. If you set your GPO to where it expires after the user fails to login for so many days, and your users don't use the domain that often, then you probably don't have the best configuration.

GPO as a whole doesn't ever expire, but specific GPO settings do have specified expiration thresholds.

I suspect you're asking specifically about Passowrds, and yes, GPO for passwords in a Windows Domain are assigned expiration dates by default. If you don't re-connect to a DC to "refresh" your compliance with GPO you can be locked out if you're relying on a Domain Account (so maybe you should consider using a Local Account instead?)

There are other related settings you should be interested in, too if you'll be out of office for an extended period of time... like consecutive failed logon attempts.