The problem is incredibly unlikely to be your switch
This very much. I use a number of SIP phones at home, initially through basic unmanaged 1Gb/Sec switches and the only times they would loose connection was in transferring huge files across the network. If you want a managed switch I'd recommend Ubiquiti gear but I'm biased as I've got loads of it due to the upgrade bug!This, it's far more likely to be something on your router/firewall. SIP ALG being one of them.
https://www.voicehost.co.uk/help/sip-alg-and-why-it-should-be-disabled-your-router