Since Piotr's answer and the discussion following it states the most important points (while an academic email address may become invalid, a private one provides no means to verify the author's actual affiliation, or even suggest the author doesn't identify with it), here's my suggestion:
- Create a PGP key+ for your private email address
- optionally add your academic email address as another identity
- Have your key signed, e.g. by
- your institution's sysadmin
- a key exclusively for your academic email adress
- Publish the key, e.g. at http://pgp.mit.edu/
- Ask the publisher to include your public key+ or at least the footprint in the publication
- The online version should even link to the key entry to make verification easier
Now everyone can easily check your affiliation while you've made sure you can be contacted in the future - you can even add alternative email addresses to you key later on (the upload can be updated), and everyone will be able to deduce that should your original address not be reachable any more, you might be reachable via one of the other addresses associated with your public key.
As an additional benefit, now both you and your co-authors can sign the publication itself, adding another level of trust that this is truly authored (or sometimes rather endorsed, if you're so honest ;) by each of you. And since you now have PGP keys anyway, you can also sign and/or encrypt your emails, making electronic communication both more trustworthy and less prone to leaks.
+ In case you're not familiar with PGP:
You create a pair of keys consisting of a secret key (which you and only you shall ever possess) and a public key (which you are supposed to make as public as possible/required). The secret key can be used to put a signature on anything digital, like messages, files, protocols, papers or other people's public key, and anyone can use the matching public key to verify that this signature stems from that secret key, and thus (hopefully) from you. Reversely, anyone can encrypt data for you with your public key that only you can decrypt again with your secret key (messages can be encrypted for multiple recipients as well if required). Since everyone can sign anyone's key, you obtain the Web of trust, a network of keys that allows you to estimate how reliable the association of a key to an actual person is without having to exchange public keys in person. (The downside is, your email address is public and social engineering is possible, but we're responsible adults, right?)
A great open source implementation of the Open PGP standard is the GNU Privacy Guard