with my little e30, the vacume throtle advance would stick and muck around when cold, (and sometimes when warm) like start, and then cut out.
I would sugest checking the "cold start valve" (on top of the thermostat and doing simple things like : fuel filter etc. just little costless things.
They probly need changing anyways.
my fix was as simple as lubricating the vacume slide, and thatwas it.
Let us know how you go and what you do. cheers and welcome