This might actually be possible in the near future with cryptocurrencies. Nobody "owns" a bitcoin wallet; spending the money inside is just a matter of having the private key. Assuming a service pops up to provide nonzero interest rates for holding bitcoin, you could grant the autonomous entity enough bitcoin to pay its own hosting bill indefinitely, then erase your copy of the wallet key and any privileged access you have to the server.
As for the actual software running the autonomous entity, all you have to do is provide an API so that the hosting providers du jour can bid on providing hosting service. Since the software uses nearly zero CPU or bandwidth, and the entity would be willing to pay above-market prices for its survival, hosting providers will be incentivized in perpetuity to register themselves and collect basically free money from the entity.
Irrational hosting providers might try to kill it, so you'd need some level of redundancy. Also, you'd want to require a TPM and a trusted computing platform to prevent recovery of the wallet key.
Anyway, that's how you'd create immortal software.