There is no hard and fast number of connections a VE can handle. It's based on the amount of CPU and RAM available. For instance, a system running standard virtual servers on LTM will be able to run more connections than a system running ASM on those same virtual servers. It also depends on things like the number of iRules you have, etc.
So the short answer is that there is no answer for your question. If you start to see a lot of these errors, then you may want to look at upgrading your VEs to have more resources. If they only occur on rare occasions, then it's probably not something to worry about.