Possible that just one string's gone bad?

I have an Epiphone EJ-200CE I bought (used, sat in the shop for a year) recently, and I've noticed that the bass E string misses its intonation often, though not always. Is it possible that just that one string is too old?

To clarify: I tune the guitar so everything's perfect. Then, after playing awhile, I notice something off in the sound. All the strings are still in tune, but the bass E gives wrong notes on the frets. For example, the fifth fret gives not an A, but more of an "A#", so it's a little high. All the other strings are fine, it's just the bass E. Neck looks like it's straight as an arrow.

Just a bad string? I have no idea when they were last changed (the previous owner died suddenly over a year ago). Never had this kinda thing happen in 20+ years, it's always been all the strings going bad/old at once, or a string breaking.