I’ve just noticed that my BDP-3 (upgraded by Bryston from a BDP-2) next song/previous song buttons don’t work after the unit has been on for a couple of hours. This is a new phenomenon that I have never seen before. I am wondering if the unit is overheating after being on for several hours. If I shut it off for a few hours, it works normally again. Has anyone else had a similar experience? 
Yes, I have had this problem with the BDP-2. I had to send the machine to a distributor to change the front PCB that holds the interface - the display and the controls. I sent the machine with one of the buttons malfunctioning and received it with all the buttons malfunctioning. At that point, I was sick of being mistreated - the machine cost nearly 4000 Euro in my country - so I contacted Bryston directly and Mr. Brian Russel, God rest his soul, sent a completely new machine directly from Canada. Apparently, he didn't like the notion of his company being represented in such a manner because one of the things they have always prided themselves on was customer service. A real gentleman, I must say, and James Tanner is no different either.
Try this - use the BDP web interface and see if the 'virtual' buttons work on screen. If they don't, the problem lies somewhere else. If they do and it's just the 'physical' controls that do not work, it is likely the contact surface on the PCB.
You can also ask Chris for assistance. He can access your BDP directly from the factory and see if it is a software issue.
Otherwise, your local distributor can possibly resolve the issue by replacing the PCB.
I must say, one of the reasons I did not upgrade to the BDP-3, apart from the cost, was that the BDP-2 works very well. My hearing is sensitive - up to 24 kHz - and I can't hear the switching PSU from across the room whereas I could hear it on the original BDP-2 that I bought. Also, the BDP-2 that I have is a later production uinit so it already came with the BUC board (what Bryston calls 'Integrated Audio Device'). Apart from more CPU/RAM resources, there isn't much difference between a BDP-2 and -3 at all.
Good luck and post here when you resolve the issue.
Cheers - Antun