Way back in '95 I was in the military until they tested me positive for pot. It was a one-time incident, and I've never done it before or since. I was separated, of course, and since then I've gotten great credit, a stable family life, and a good job. However, I recently applied for a contract job with an employer on a Navy base, and they require me to pass a security clearance. I'm betting they won't pass me, as I received an other-than-honorable discharge back then. 

My question is - does the Navy have an unforgettable memory in regards to these kinds of things? Do they never forgive or take into consideration events/progression since then? I mean, what if you had an OTH back in 1968 - would they say 40 years later, "Oh, you had an OTH discharge; sorry, you're not getting clearance"? It seems a bit ridiculous if this is true, but I wanted to get some input. 

Has anyone run into this? What can I expect?

If you apply to get upgraded discharge, make sure you ask for an honorable discharge, not general.  Also ask for a change in the reason for discharge to "convenience of the navy"  Show up in person with character references, written or there with you, employment references and any supporting documents.  Also make sure you request your military record.