I had a similar issue this summer.
Unplug the IntelliChlor (IC) from the IntellipH (IpH) controller. Unplug the IpH controller from the Power Center. Then plug the IC into the Power Center. This troubleshooting step will eliminate the IpH from the equation. If the symptoms go away, it's the IpH. If the symptoms persist, the problem is not the IpH.
Since you're getting the same (or similar) symptoms with two different ICs, it's most likely not the IC. I, too, had a backup IC and did the same test. The problem happened with both of my ICs.
So it wasn't my IpH. And it wasn't my IC. I replaced the Power Center circuit board, and the problem went away.
If after the steps above, it still points to the Power Center, order this from Amazon and install it.
If that solves the problem, then you're done. If not, then return the board to Amazon and report back for further troubleshooting.
If the above steps point to the IpH, report back for further troubleshooting.