I currently have four types of ASICs in my mining rig: Bitfury, BFL, Antminer, and Gridseed. The Antminers are self-contained, while the others all run off of the Raspberry Pi in the Bitfury rig.
bfgminer seems to work well enough with my Gridseeds for scrypt mining on Multipool, but it seems to have problems on the SHA-256 side when the pool switches coins. It gets stuck, and never appears to get unstuck. The Antminers shipped with cgminer, which doesn't appear to have this problem.
Supposedly cgminer was never going to be updated to work with BitfuryStrikesBack rigs because they were limited to running on the Raspberry Pi, connected through its GPIO port. At some point, though, support was added for the Bitfury-based hardware from Black Arrow, which is AFAICT functionally identical to BFSB hardware (they both support four groups of hashing boards per RPi, with the chips in each group chained together over SPI). I built the latest cgminer yesterday, tweaked the config file a little (took stuff out, mostly), and fired it up. It's working much better now with Multipool. It's been running since sometime yesterday evening, switching between coins (network difficulty keeps switching from ~11 billion for Bitcoin to somewhere in the low hundreds of thousands for the SHA-256 altcoins) without an issue. As a bonus, it's also tweaking speeds on the Bitfury ASICs to squeeze more speed out of them while keeping errors low. If a chip got pushed too far with bfgminer, it would start spewing nonstop errors until it was restarted.
With all of that said, is there some reason why the SHA-256 side of Multipool runs better with cgminer than with bfgminer? Given that the scrypt side of Multipool works fine with bfgminer (good thing it does, as you can't mine scrypt at all with recent versions of cgminer), this seems a little odd.
The SHA-256 pool is the only pool that still disconnects when switching coins, this is necessary due to the BTC hash being proxied to another pool. That is likely the source of your issues. That said I also run bfgminer with my SHA gear and I've never had any major issues with it.