Just ran across this question, and can give you a couple of suggestions.
If you're trying to gauge when to move to a bigger instances (vs. increasing the size of the databases) when you're getting close to hitting some sort of resource limit: Memory, I/O and CPU all have the ability to limit your performance.
The symptom you mention in the question may be a symptom that you're using more and more memory - memory used for cache & buffers are being reclaimed for other uses. Upgrading to a large instance type will increase the amount of available memory.
The chart that Rolando posted should give you a good guideline as to the number of available connections - if you're hitting those limits, then it's time to upgrade. Available connections are directly related to available memory, so hitting connection limits means you should upgrade.
If your CPU is averaging > 50% or so, you might want to start planning on an upgrade.
Finally, if you see consistently high I/O you may want to consider a larger instance (generally, the more powerful the instance the better the I/O) or using provisioned IOPS.