Battery light came on in my 2001 mazda miata replaced new alternator, 4 weeks later battery light back on car loss of power, removed new alternator took back to where purchased and had it tested and was told it had lost voltage down to 11v . all belts are in working order and the batter voltage is correct. checked all connections three times to make sure all are in good order.

INSTALLING NEW BATTERY.WHEN DISCONNECTING BATTERY CABLES THE ECM WILL LOSE IDLE CONTROL MEMORY.TAKE TO MAZDA DEALERSHIP LET THEM RESET ECM SO CAR WILL IDLE STOP STALLING AT STOPS.

Where was it stored? If corrosion is the issue, battery cables, wiring to alternator, alternator itself, battery terminals, fuse block, anything moisture got to sit on or near for more than a week or so. Miatas hate water in my experience.

The power loss light goes on as a result of the alternator being bad.
Are you getting 'lifetime' guaranteed rebuilt alternators to replace the old ones?
If not, then the quality of the parts may not be good enough to run in your application.

Are the connections clean and shiny when removed?

HI, you will find the battery under a panel behind the seats. changing it is done like any other vech. remove the negative cable first then the positive, remove the hold down and carefully lift it out.

SOUND LIKE CRANKSHAFT SENSOR OFF.TOO MUCH GAP FROM CRANKSENSOR TO CRANKSHAFT PULLEY PULSE WHEEL.

The alternator is loading up too much for some reason.
Had the same issue on my friend's 2001 Mazda Protege. Turned out the voltage regulator in the alternator was faulty. Had the alternator rebuilt. A week later, it acted up again! There is apparently another issue, but I have not been able to figure it out.
Unfortunately, I don't have a clear answer for you, but, one's thing's for sure. Mazda has to stop using crappy Ford electrics in their cars.

Alt shoud be putting out 14 to 15.2 volts.

Only way to completely empty tank is to remove it. there is about a two gallon space between the pump and tank bottom where condensation can build up. You can partially drain it by disconnecting the fuel line and turning the key on. The pump will empty tank (don't run the pump after fuel is mostly empty or it will burn out) Also make sure that hose is secure so that fuel dosen't end up on the ground. After you have finished, put the battery on a charger and bring it back to best charge...Alternator will not and cannot do that.

Batteries can have a dead cell in them, meaning there is sufficient charge to run accessories and the "check glass" may look fine (dark green in color on maintenance free batteries), but one dead cell in the battery indicates replacement time.

I have a 2001 Mazda Tribute. To change the alternator; the factory procedure at the dealership says to drop the sub-frame from under the front of the vehicle. Then everything is accessable. The tech at the dealership told me how they do it: (Its not easy!!) 1. Remove the right front tire 2. Remove dust pan from right front 3. Remove the brake caliper and caliper bracket 4. Remove the 2 bolts from the half shaft support bracket 5. Remove the half shaft axle assembly 6. Remove the serpentine belt 7. Remove the 3 bolts holding the alternator in place 8. Remove the 3 bolts holding the alternator mounting bracket 9. Remove the alternator mounting bracket 10. Remove the electrical connection on the alternator 11. Remove the alternator by turning the alternator until it will come out of the opening 12. Repeat process in reverse for installation. I did this twice in two weeks because of a bad alternator. The studs that are spot welded on the half shaft bracket will try to keep you from being able to remove the alternator. The left stud on the bracket popped out, when we were removing the alternator and it seemed to make it easier to get the alternator out. I just put a lock washer on the back side of the stud when I mounted the half shaft and it worked fine. Good luck