Transmission cooling line popping out of radiator

Make sure the cooler line goes into the fitting perfectly straight, so that the flange on the line clicks behind all three points of the retaining ring (see pic). It may take substantial force to push all the way in.
Trans Cooler Line Fitting
Note that, unlike in the pic, all three parts of the ring should protrude into the fitting the same amount.

When installing the retaining ring onto the fitting, GM suggests rotating it in place rather than pushing straight on, so as not to stretch the ring.

Make sure the flange on the tube is in good condition, flat with nice crisp edges. If the flange is bent or rounded on the edges, the retainer may not hold it in place well.There should be a plastic cap that snaps over the fitting. I don’t know if this is just a dust cover, or if it actually helps keep the retaining ring from expanding and allowing the tube to come loose. According to GM, there should be a yellow identification band on the tube that should be hidden within the fitting when properly connected. If that band is visible outside the cap, the tube may not be clicked in all the way.

The cooler lines appear to be clamped to the engine. Make sure any engine movement isn’t causing a tugging on the lines.