I checked for a prayer room in Suvarnabhumi Airport (BKK).
Is it accessible during transfer?
There is a prayer room available in the international part of the airport. Based on the map, it appears to only be accessible to travelers awaiting any international departure. International arrivals and domestic arrivals/departures do not have access to this area unless you are connecting to an international departure.
There is also apparently a second prayer room, not indicated on the airport website or map, in the domestic departures area. This Muslim-friendly guide to Suvarnabhumi Airport has details, along with some other helpful information about the airport.
I have confirmed this with the helpful "live chat" feature BKK is kind enough to provide on their website. They inform me that: "1. It's on the 2nd fl. near Concourse C. and 2. on the 3rd fl. near Concourse E."