Will transplanted hair fall out if you stop using Minoxidil?

The true value of hair transplantation is that it is permanent (once the graft has taken). We are moving hormonally insensitive hair from an area of high donor density and transplanting it to an area of relative deficiency. This hair will behave as if it had never been moved. Thus hair which you did not need Minoxidil to preserve in the first place will be replacing the hormonally sensitive hair you have lost (are losing). Altering your Minoxidil regimen will only affect the native hair which you were losing not the grafts. As always, discuss your concerns with a board certified plastic surgeon (ABPS) with experience in hair restoration.

Topical minoxidil is a medication used to grow new hair.  The medication does not cause hair loss.  

A few studies have shown that Minoxidil applied to the grafts can potentially help initiate early graft growth. That being said, your grafts should still grow even if you choose not to apply Minoxidil to the graft zone (assuming good surgical technique and that you followed all postoperative instructions as outlined by your surgeon). Grafts usually begin to grow starting at around 4-6 months, and full results are seen by about 12-14 months. The grafts do take on the characteristics of the donor area, so assuming that your donor area is not effected by the miniaturization process, these grafts should be present long-term. It is important to note that a hair transplant does not stop the hair loss process, and the preexisting hair will continue to thin over time. Minoxidil and Finasteride can potentially help the preexisting hair from thinning and may give you the best chance for stabilization at this time. I recommend discussing these medical options with your hair transplant surgeon.