on my ESP Eclipse i'm having some general issues with the guitar staying in tune, particularly on the low E string.

To me it seems as if the string isn't sitting in the nut properly and therefore this could be the reason, but could there be anything else that is making it go out of tune so easily?

a picture of the nut might help here to confirm it.

check the intonation, stretch the strings. and all the usual stuff that i`m fed up of repeating.
Make sure there are enough wraps around the tuning peg too.

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There's a sticky now on restringing guitars. It shows the most accepted/preferred method for non-locking tuners and show help a lot.
Moving on.....