This, usually, is a memory leak at the code level of some kind, or at least used to be before garbage collectors got more robust.

That's usually the case, actually. If you're an SA on the box, though, you can look for a few things. First, regarding deadlocks, you want to look in the server logs. If you're not SA or equivalent you won't have access.

However, deadlocks, on their own, shouldn't lock out the system unless the app's error controls are very weak. A deadlocked query will report that it was killed and should be resubmitted. If you're logging your db call errors from the app side, you should see them there.

During the lockup, you want to try to look at sys.sysprocesses and see if there's any long running queries. If there is, you have some ammo for discussion with your DBA. Again, you'll need SA rights. If there is, you want to look for either blocking chains or a query that's just taking a long time with no blocking. If you find a query running long with no blocking I recommend you starting up a trace to locate the problem child (RPC and ad-hoc queries, get the starting and ending so you can check durations) and health check those procs for optimization. If there's blocking you've probably got a lot of edits going on simultaneously and those need to be optimized and tightened in scope.

If you don't see this telltale sign, I hate to be the bearer of bad news, but it's most likely either app or network. If the server is responsive, there are no long queries, no blocking chains, and no pressure (I/O, Memory, CPU) then the DB server is healthy.