If it's a loose belt you would normally hear it screeching.
Alternators should give a good voltage from very low rpm if it's in good working order. (That is one of the benefits of alternator v dynamo)
I would suspect either loose or corroded alternator connections or the alternator itself.
There are lots of companies who will test and recon an alternator for you.
BTW can't see how this could be an ECU fault.
