Are you comfortable logging into the modem/router and checking the logs? They may give some indications as to what's failing. That's the first thing I'd check. There may be a place in the router setup to change logging levels (how detailed the logs are).
I'd also consider running an ethernet cable just temporarily, to see if it is only a local WiFi issue or not. If you have the same problems with wired, you know it's not a WiFi problem.
Turning off the firewall would be a logical troubleshooting step, but I'd be leery of leaving it off for any length of time. Out of curiosity, is this a separate hardware firewall, a firewall built into the router, or ?
One thing it could be is a DHCP problem. That's the protocol whereby the phone or device asks the router for an IP address. The router than issues an address, with a "lease" (expiration time). When the lease expires it should be automatically renewed, but sometimes s@#t happens. Rebooting the phone would force it to issue a new DHCP request, temporarily "fixing" the problem. That's just one possible problem, though - it could be lots of things. A DHCP problem should show up in the logs, though.
It's possible you're getting radio interference with the WiFi signal, but other than trying it over copper ethernet, I'm not sure how you could tell without test equipment. Are you aware of any new electrical equipment that might be interfering? I've seen one case where a leaky microwave oven caused WiFi problems, but other electrical equipment could cause interference, too.
FYI, I'm not very familar with home networking equipment. Even with the commercial stuff, though, troubleshooting WiFi problems really sucked, and that's with test equipment and very good logs. That's not even considering the security issues with WiFi. I did not care for it and would always go with copper or fiber whenever possible and still do at home. I'm a bit of a fossil in that regard, I think.
I'm probably overlooking a lot, but that's all I've got right now.
Good luck!
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