Trouble cranking

Battery and starter relay have been replaced but the truck sporadically cranks. Sometimes the engine will turn over and crank every time I turn the key. Other times, it will crank once and if I turn it off, it won’t crank again for the rest of the day. There doesn’t seem to be a noticeable pattern. When the truck is running, there are absolutely no issues at all. I have a new starter but haven’t replaced it yet. I was hoping for some advice before I took the next step. After reading that it may be a glitch with the anti theft system, I followed the advice on unhooking the battery and then letting it sit overnight before reconnecting. That worked sometimes but not 100%. What might be causing this or what should I be looking at to try and locate the source of the problem?