We have indications that we can.
There have been many people who have apparently embraced the faith sincerely and wholly and then fallen away at some point in their lives. There have been many people who have spurned the faith of Jesus for Eastern mysticism or pagan rites.
If we spurn God, then we spurn His Grace, and lose our faith. The evidence is there.
Faith, by definition, is, well, faith. How can we spurn something that we have faith in. The evidences isn't as it seems.
1Jo 2:19 They went out from us, but they were not of us; for if they had been of us, they would [no doubt] have continued with us: but [they went out], that they might be made manifest that they were not all of us.