The only difference between Zoiper Pro and Free is the larger codec list which could lead to some packets being filtered by SIP ALG or some firewalls with UDP transport, because the packets could become very large in some cases. Or the presence options. In general Zoiper5 Free and Pro are exactly the same.
When your firewall or PBX starts filtering the packets, this could lead to negotiation issues which could look very similar to what you have described.
I can also suggest that you first try disabling the "Subscribe Presence" and "Publish Presence" options from Zoiper -> Settings -> Accounts -> select your account -> Advanced. Some server reject those and after some rejection attempts could block the UA for some short amount of time or stop responding overall.