is that normal for alternator to last only 27000 miles?

The question is, where did you get the alternator? What is the quality of the alternator? A Honda factory remanufactured alternator has a three-year 36,000 mile warranty. These units tend to last a really long time, beyond their warranty period. Acquiring a lower cost lower grade product at a local parts store will yield probably less reliable results. You can't make assumptions of product quality, and yes -- you do "get what you pay for". Certainly, I would recommend another opinion - see this link to find a shop near you. https://repairpal.com/auto-repair-near-me