Why would DHCP fail so often on a domestic network?

Many home routers provide an interface to list the current DHCP clients and lease expiration times. The period of the lease renewal is also usually configurable. If you see that your device that loses its connection to the internet still has a valid lease (unexpired) in the DHCP clients table, then that means you will have ruled out DHCP as the cause of the problem. If, however, you see that the loss coincides with DHCP lease expiration, then bingo you have found the cause and will likely need to modify your DHCP settings to use a longer lease period.

If you don't have access to the administrator interface for the router you are connecting to (for instance, if it is not a manually created network but something managed by an internet service provider or similar entity) then my guess is that DHCP issues are very unlikely, as the ISP will choose settings that will be designed to "just work" for most customers. In this case, try other avenues of investigation, like - are you connecting to 5GHz or 2.4GHz channels? Are there multiple access points for the same network and when you move your device closer to one of them the connection is more stable, whereas when you get in range of the other node it drops? And so on...