I used to be in the exact some boat as you. I still have this problem occasionally, since I get periodically more busy with real life/passion work and I experience a sort of activation energy associated with booting a game up (relatedly, I feel a bit guilty when I'm actively doing something unproductive and leisurely, which ironically leads to me passively waste a lot of time on the internet. Go figure).
However, in the last two years, the time has always come around where, even after a month or more, I can bring myself to get back into an old playthrough. Want to know what the key has been for me? Quitting multiplayer games. Yeah. See, I realized that most of them weren't worth the huge blocks of time I was spending on them, especially since the only good multiplayer games I was playing (e.g. Tribes, Quake) are as dead as this forum's hope for a renaissance of incline. Also, if you're playing a MOBA or an MMO, get yourself out of that hole ASAP. You'll look back and wonder what in god's name was worth that amount of investment, and hopefully not of the financial sort.
Since I did that, I've had a lot more reason to actually finish what I start, provided I was enjoying it. Sometimes there are lulls in engagement (looking at you, New Vegas strip), and it's tempting to drop a playthrough for a while, but when all you have to look forward to are other singleplayer games with a beginning, middle, and end which will require a similar sort of commitment, it's less tempting to continually drop games and start new ones. Not only is it easier to dig yourself out of a rut when you're only playing singleplayer games, but every moment spent gaming is experiencing something new, or revisiting something intentionally -- you're never just "clocking in" and doing the same thing you were near-mindlessly doing for the last 10 weeks. I still play a bit of MP FPS here and there, but it's pretty sparing and just for a few minutes at a time. If I'm feeling unmotivated to continue a long RPG playthrough, I'll download a nice, short oldschool FPS like Doom or Quake and blast through it in a couple of days for a change in pace, then get my head back in gear to continue. If I keep stalling and can't find the energy to get back into it, I probably wasn't enjoying it that much anyway, and I can actually know that for a fact because I don't have any other gaming commitments eating up my attention.
I'm sure some people could balance the singleplayer/multiplayer thing better than I did, and maybe you're getting much more enjoyment out of the latter than I was (and playing better/less dead games). I just know that quitting them almost entirely was like waking up and discovering this whole world of classic games I had never allowed myself the time to play. I've been like a kid in a candy store ever since.