Facelift redo - Can it be redone by repositioning the fat and tissues without losing skin?

Only on the basis of in person evaluation or, at least, series of good photos, one could give you a meaningfull answer. It would be in your best interest to have a consultation with a bord certified plastic surgeon with expertise in facial rejuvenation and fat grafts. Good luck.

In modern plastic surgery, it is uncommon for a surgeon to perform a skin-only facelift. You may want to get a copy of your operation report and also your before-and-after photographs before seeking a further opinion.
Revision or re-do facelift is an art unto itself. The surgeon needs to know the details of your prior surgery, analyze your present changes, and plan the appropriate procedure. Various types of deep plane facelifts used with different types of fat grafts and lasers give the modern surgeon beautiful results (see link below).
Yes, it is possible to revise a facelift and get better results! I would suggest you get two or three opinions and choose the surgeon you feel most comfortable with. There are excellent plastic surgeons out there who can help you wherever you are!!

A facelift, if correctly performed, revitalizes the face and neck area by selectively eliminating specific pockets of localized fat (such as jowls) while lifting and repositioning others (such as the malar fat pads and nasolabial folds) and tightening deeper drooping structures (such as muscles and connective tissues, namely the SMAS), ultimately topped off with a deftly executed re-draping of the skin.

I hope this helps,
Best of luck !

Randal Haworth