When alien Greys, Reptilians, or Arcturians possess a person by a suppressing their mind and taking over the body remotely, will all memory of what happens during that possession be suppressed, and how long can that possession be maintained?

The memory suppression is automatic, and part of the process involved. By pushing aside the conscious mind of the human, they prevent the deposition of memory at the same time. In effect, the body is rendered available to be controlled separately and under the direction of the extraterrestrial doing this psychically. The body will be manipulated and perform however is desired with the mind of the extraterrestrial in charge and there will simply be no recollection of what took place once the extraterrestrial consciousness lets go and departs. This can be done for a day-long exercise, but is difficult to maintain for a longer period, so it is ideal for short-term ventures and target assignments that can be done quickly, although it is possible to repeat the intrusion at frequent intervals to accomplish an objective in stages, doing portions over many days or weeks to get a certain task finished bit by bit.