If he proves it everyday, why do you doubt it?
It sounds to me that you are doubting your love for him.
No, it is called "Trust Issues" . . Either it is a problem with you where you have had many times where someone has "Slighted" you and now it is part of your character to "Not Trust" . . . OR it is because you have caught him in several lies and understand that it is Part of HIS nature to lie . . .
So . . . Which is it?