I was talking about foreign ATM cards. The limit on these was/is 8.000/day.For BBVA account holders, the limit the last time I looked was 25k (but only from a BBVA ATM); this is the minimum amount you can take out from the counter - if you ask for less they tell you they're not allowed: you have to use the ATM.
I'm in the same boat as you, I fortunately haven't had to use my card recently in an ATM here, but the need could come up. I'm sure your card is fine. I would try to use Link, if that's an option, the fees are lower.
But anyway: I've also had the problem with the amount, if you ask for too much initially, and go lower as the ATM suggests, it will never work. I've complained about it to zero effect. Try with say 4000 pesos (yes, I know, the fees will kill you) and then go higher. At Link ATMs I used to be able to get 6000 pesos in one go. Banelco wanted to give max 4000 pesos and charge 10% of that in fees. That was a while back, of course. In any case, the ATM should be able to dispense 40 banknotes to you, and the hopper will be filled with 500-peso notes at a minimum.
There were also certain ATMs, of the same bank (Banco Ciudad) as other ATMs I successfully used, that would never, ever, give me any dosh. I also remember that Banco Ciudad at one location I used "upgraded" their 2 ATMs, one worked for me, the other not. Banco de la Nacion also uses Link, and has never ever wanted to give me money. It also waited about a minute to give me my card back. YMMV. AWA.
It has nothing to do with how many noted the ATM can dispense. Banelco is a cartel and they set the rules and fees. They used to (and it seems they still do) limit a single extraction to 4-8k and the daily one to 8k. Obviously they still charge you 10USD per each go. The banks have few sources of income and they are taking advantage of the few confused foreigners left in the country.