No, your 15 days don’t vanish completely.
You only “spend” the Alpha Points you’ve accumulated — for example, 210 points on one airdrop.
After that, you keep earning points daily as usual.
So yes, realistically, if each airdrop costs 210 points, you can join around 2 per month (every 15 days), as long as you maintain the same daily point rate.
Pro tip:
Keep farming 13–15 points daily to always stay ready for the next drop.