What happened to the charge rate at the battery when replaced the alternator? Bad battery cable can create enough resistance that voltage and amperage at from the alternator to the battery can be reduced. You could try something like an additional cable from battery to the alternator source (starter). Just use a jumper cable. If this happens all the time it should be easy to do things like add temporary extra ground to the engine etc. Look for evidence of heat (resistance)at accessory leads from battery. Check plugs where accessory leads pass through for same. Good Luck.