There are a lot of options here for addressing the issue that haven't been tried, or at least haven't been reported as tried. Have you confirmed that the modem isn't configured to close connections after a certain period of time? Being able to DHCP properly has no relation to this issue.
It seems other people have this issue with Pace modems.
"I received this modem after getting an email offering to upgrade my 2wire modem.Since then I have had constant problems dropping wifi calls on my ATT cell phones." --
https://forums.att.com/t5/AT-T-Internet-Equipment/Pace-5628-ac-wifi-calling-issues/td-p/5119266
"Wi-Fi calling is what tipped me off to the problem as well. Both my phone and my wife's started having issues at the exact same time so I knew it had to be a network issue. I kept chasing non-existent Wi-Fi issues until I just happened to do a speed test and saw that I was only getting 50Mbps. That ultimately led me here.." --
https://forums.att.com/t5/AT-T-Fiber-Equipment/PACE-11-1-0-531418-DMZ-Issue/td-p/5700776/page/9