Bricks, Masonry, Asphalt and Concrete - Mounting a doorstop in brick...

As a janitor/maintenance guy at an elementary school, I have been asked to mount a heavy brass doorstop/catch, with a hook-n-eye that holds the front door open for recess and "school's out" time. The stop goes in the wall, and the eye gets mounted on the back of the door. The problem is I have to mount the stop in brick. Really old brick. And I have little experience with masonry/brick, etc.

My first try failed. I drilled holes with a masonry bit, inserted the anchor thingies, and screwed the stop in place. Looked great, but 2 days later it busted out of the wall, partly shattering that brick. Now I have to remount that one and do three others... I have more of them same hardware, plus a bag this patching cement stuff called Rockite.

My plan of attack is to drill the holes, mix the Rockite, put it in the holes, then shove the anchor thingies in there, let it set a couple of hours, then screw the stop in place.

Am I about to face disaster? Or is this the right thing to do.
I am new at this job, and I don't want to screw up and get fired.
Half kidding.

A lot depends upon the door and the wall makeup. With a heavy door and a cavity wall, I would use a toggle bolt through the brick.

If it is a heavy wall and solid masonry construction, I would use tapcons. If it is a light to medium door, I would also use tapcons. In both cases, the tapcons should go into the mortar joint, not the brick.

So you are saying put it in the mortar, between the bricks, and not in the brick itself? I don't think I can use toggle bolts....

Is the mortar actually stronger? This is brick from, like, 1910. Does that make a difference?

Thank you for actually responding.