I can't speak specifically to Chromebooks as I don't have much experience with them directly.
However; I have had an issue on my wireless network where I've had wireless devices (All-in-One machines mostly) that will "see" two APs simultaneously and will go into this bizarre behavior where they will constantly flip back and forth between the two APs. (The APs all share a common SSID.)
For the particular case I had, I ended up changing the SSID on one of the APs and that solved the problem. The proper fix would be to adjust the power levels on the two APs to guarantee that the AP in the room with the device is always the strongest signal.
I don't know what your particular topology looks like, but if you've got two APs in close proximity to one another sharing the same SSID, you might try temporarily disabling one and seeing if your condition improves.