Yeah, I've got a "halting BizTalk" issue I'm looking into.
I've got a fair sized application here with a couple dozen orchestrations handling all sorts of inputs and doing all kinds of SQL operations.
Every now and then, for no apparent reason, the whole process just stops. No warnings, no errors, nothing in the event logs, it just all stops. Nothing strange in the PerfMon counter log (typical system and BizTalk counters being monitored). The only known fix for it is to restart all the hosts involved. That tends to "kick start" the process to continue from where it left off. Obviously not a long-term solution.

So far, your comment about the SQL Adapter and the increased default isolation level is the best indicator I've had about which direction to look in, my main thoughts besides that are that I might find something like a deadlock somewhere in the SQL.

Very mysterious.