Scabs even after a month. Can transplanted hair fall out with roots during the first month?

You will lose your transplanted hair as well as some of your native hair weeks after surgery. You may look worse before it starts to look better. It may take 6 to 12 months to see the results of a hair transplant surgery. It is always a good idea to follow up with your doctor for a recheck if you have concerns.

I get asked this question often and this also happened to me personally.  After 3-4 days, the follicle cells have become for the most part a permanent part of your dermis.  What is coming out is most likely coagulated blood cells (and hair shaft of course).  

It is completely normal to lose the transplanted hair in 3-4 weeks after a hair transplant.  In fact over 90% of people lose their transplanted hair shafts and hair follicles enter their resting phase before they can start growing in 2-3 months.