If it involves debit/credit card transactions then you start rinning into the PCI-DSS regulations, so unless you're willing to take payments in crypto doing it yourself gets problematic. Even cryto would be nearly impossible since by its nature those are a more push trasaction where a recurring transfer would generally be a pull from the payee to the paypor.
That's not to say it's impossible, after all e-commerce is a thing, but any kind of stored payment transaction puts you in a whole new world of liability and makes you much more of a direct target for thieves than just a passive 'send money here' style donation page would.