I've found that in 90% of the cases where packets are dropped randomly on a consumer-level access point, the automatic channel selection is to blame. Go to settings, select a static channel number, and the problem disappears completely.
In my case it doesn't seem to be the wifi side of things, but the routing side of things that's causing trouble. I can consistently ping the local AP itself, but the connection to the internet has periodic dropouts.
90% is probably too generous. I tried static channel selection on two wifi routers with the same issues described here and it does not fix the issue.