As there is a sufficient reserve of oxygen in our pond's water to last for days, weeks, a month or more(?), I leave our aerator off until an ice cap forms that will support our dogs and me. This could take a few days when we have very cold cold weather; it could take weeks.
I then fire up the air pump with the diffuser relatively close to shore, and in a few hours, there is an open hole. The rest of the only 1/4 acre pond remains frozen enough to support all of us. My Aussies edge up close to the open water, realizing that they could go in for an unwanted swim, but that they also can make it to shore. The dogs some times toss their tennis balls into the open water, wait back from the edge of the ice for the balls to drift in close, then stretch out and grab the floating toys. It seems like this is particularly great fun for them. Once in a while, in they go. But they happily swim to shore, shake off, and zoom back out onto the ice.
My experience has been that the ice at the edge of the hole remains rather strong.
You might try shutting down your aerator for long enough to build thick ice, then restarting it.
