Hi,
You can diagnose by shutting the phones down for a short period.
As for your neighbors access points, channel hopping is a possibility. But if the wireless is setup properly there should not be a problem with having multiple units on the same access channel. If there is then someone that has a failing unit or intermittent transceiver is at fault. It makes this type hard to find without proper equipment. I've seen some failing adapters create collision problems but these type of errors are rare.
Do you by chance have any other wireless devices? What type of wall construction do you have for exterior and interior? Your neighbors could have other wireless devices (phones or whatever) that are interfering with your access.
I live in the country so I don't have to investigate anyone else but my devices. I've had wireless transceivers for phones that have caused problems. New enough to exchange for a new product.
I've been wanting to replace my thermostat with a wireless/Ethernet unit. Leaning towards the Ethernet unit for these same reasons. Plus the fact that the wired will have backup power from the server. To much to do in so little time!