@Allymadeathing As a disclaimer, I did not use an academic letter for vet school (I only applied to one school that did not require an academic letter so I didn't bother) BUT I do have a general plan for things like this and have used it over the years for references and it has worked well.
I've been out of undergrad for 12 years and grad school for 4 years. Over those experiences and work experiences, I try to identify someone to stay in touch with. For example, from grad school I have a professor that I had TA'd for and saw as a mentor. Over the last 4 years I have touched base with him on occasion and have gone by his office when I have been near campus just to say 'hi' for 5-10 minutes - nothing onerous, just something (email or something) every 4-6 months. I also did this with one undergrad professor and a manager from the job I had before Peace Corps - those references ended up being really helpful for me when I applied to grad school 6 years after undergrad. On the flip side, I have a couple of interns from as long as 6 years ago who have done the same with me and I recently wrote one a recommendation for a new job that was twice removed from her internship. I would be comfortable writing a letter of recommendation for any of those who have kept in touch with me, but less so for the ones who haven't - mostly just because I feel like I don't have any connection to them.
Since you have some time, I would maybe identify a couple of professors (just in case one isn't responsive) that you could see yourself maintaining that kind of contact with. Who knows, it may be beneficial even further down the line as a professional reference or if you decide to do a fellowship, etc.
Another thing that might be helpful, if you have something you are doing for gap year that might require a letter of recommendation, ask that same professor(s). I save all the letters I write - I had written an LOR for that intern I mentioned above 3 years ago for her first job after the internship. I just pulled that letter up and edited it with more current information for the one she needed last month - a lot of people who write letters will save them, so if they have something to refer back to that reminds them of how great you were, that would also be helpful.
Just my opinion, but when you are applying to jobs after having many years of experience, it's a plus to have a history of references that span further than your most recent employment. People definitely get jobs without it, but I've had a couple of people comment favorably on it over the years and it certainly can't hurt to have more options when you need a reference!
