I just discovered ME three freaking months ago, and it's been so much fun to fall in love with the games -- I've just done 3 playthroughs so far but it's been so rewarding and so much fun.
To echo the OP, I definitely felt profoundly sad after ME3 was over the first time I played it. Yes, I was dissatisfied with the ending (which even in EC form felt visibly rushed and illogical to me), but I was okay with it anyway. I did find the final montage powerful and quietly moving in spite of the flaws in the storytelling, too.
I was more sad to be "finished" one more time with this wonderful universe and its rich characters. I missed them in ways that I missed Harry Potter after 7 books, or Jack Aubrey after 20+. The way I missed the Buffyverse after dozens of hours, etc. By the time each playthrough ends, we've spent dozens, even hundreds of hours in Mass Effect's world. The game is that rich to me. So even though I didn't love the ending, I did feel a sense of completion and loss. I would miss these characters until the next playthrough.
But then a week later, I started all over again, already thinking about decisions I might have changed, paths I might have taken with a different Shep. So that also means we get that joy of replay, that feeling of rebirth when we go back and restart. Anytime we want Shepard alive again, and Shep's loyal band of misfits and squadmates, the game is waiting.
Also, OP, I hope you reconsider playing it the same way and only the same way each time. Because it's so much fun, and so much richer, if you vary your Shepard even a little.
Even if you really feel you need to build the same Shepard, for instance, that is an avatar of you once again, as others suggested, next time change his origins, his background, his class and abilities. Think about small ways to change his decisionmaking that fit into that. How would this new Shepard react in the game's hundreds of scenarios? More kindly? More impatiently? More brutally? Etc.
I'd also suggest that next time you play through the trilogy, that you really explore the squadmate relationships. Consider a different LI, or simply take different team mixes with you on the different missions. The last time I did that, I found ME2 just freaking delightful. To take Legion and Tali on missions, or Kasumi and Thane (my favorites, the perfect mix of gravity and lightness), or Grunt and Garrus, etc., all these different combinations, made the game fresh and new for me.
I'm just finishing up an ME3 playthrough now, and this time my Femshep was more cautious and guarded, more renegade while still being honorable, and even knowing the 'beats' of the story, things changed incredibly for me in all these little ways. On Rannoch in the past, I've saved the Geth but doomed Tali and the Quarians, I've brokered peace with both, and this last time, I watched Tali shoot Legion (something that had never happened for me before in the game).
The game is sensitive enough that if you just change a few things about your character each time, it's going to continue to surprise you. And I really love that. And then you don't have to let that melancholy linger because this world is always waiting for you to return to it fresh and new and full of hope, just like Shepard.