Yes, it's possible. You just need a few rules. All miners must sign their blocks. All miners must "register" their public key before they are permitted to mine with that key. Blocks signed by the same public key are invalid if they are too close together by some rule.
The trick is controlling the registration system so that a single party can't just register thousands of public keys. You can do this by charging a fee for registering. You can also do this by having human approval required in the registration process.
You can design the fee so that if you mine for a month, it pays your fee. That way, only people who intend to mine long-term or invest in the coin will be able to mine. This will protect you somewhat from hit and run attacks.
However, for the record, I think the entire reasoning behind this is backwards. ASICs make coins more secure because they increase the investment required to attack the coin, just as this scheme would do. With ASICs, it's already done -- people have to invest in the coin to attack it.