I have not had dropping off on Radio iPlayer, but I certainly have on TV - I think when their servers get overloaded. Is it possible you are suffering from a lack of bandwidth at the BBC end?

Cinema/Music: Trinnov Altitude32 8-16,218,Cloud 4 channel, Marantz UD5007,DSP5200SE(2+C),DSP3300(4),DSW(2),271,MShort Ceilings,AppleTV 4K
TV: Marantz SR7013 Wharfedale Diamond 9x4+Celestion(C)
Music: Roon,i7NUC8gen,QNAP TS253A, Sony Scala, MS200, Garrard DDQ650,Wharfedale Diamond 12.3
Kitchen: AD88 (bluetooth via i80).