So I've laid out my situation below. If anyone has any helpful insight, I'd definitely appreciate it!
We have 2-4 computers wirelessly connected to a router within only a few feet (100% signal for all computers).
Every few hours, although the computers indicate connectivity (no warning signals or such), the internet simply stops working for all computers.
Restarting the computers and repairing connections don't remedy the issue.
Only by unplugging the router for a minute or two is the internet restored.
If I keep my torrent program open, I believe I've noticed that it maintains the internet connection.
Possible factor to consider:
The downstairs neighbors' wireless router sits pretty much right below ours.