Am I missing a part? This is a 68 road runner manual brakes

Let's see if you can see this image

https://www.flickr.com/photos/153614762@N02/?

there should be a rubber piece that goes on the end of the rod,there is a groove that the rubber fits in, it is what holds the rod in the master.

did you replace the master recently?
manual masters have a grove for that rubber, but power ones might not, so even with the grommit it could pull out.

have your parts house cut a piece of vacuum line of the right dia (7/16 iirc but don't quote me), just long enough to slide on the end of the pushrod into the groove on the end like in the pushrod in the pic. The tailor made ones have a thin/shallow groove lengthwise along the neoprene piece which might be to let the air out as it is installed into the tapered blind hole or it might be nothing & just from how it was held when it was mfr'd. Lube it, as it is a tight fit.

I do have the rubber piece It stays in place but if I pull back on the pedal it will come out

I looked at my cuda and this cant happen with that setup

It seems a safety issue. A local car had this happen on the track and had no brakes with disastrous results

I was going to weld in a bracket to create a stop to prevent it from being able to be backed out.

I was wondering if I was missing a part on the pedal assembly

Look down in the rear piston "thimble" in the back of the MC & there must be a shallow but wide circular groove about halfway down for the neoprene piece to lock into as opposed to it being a smooth taper like a sewing thimble, otherwise it just pulls back out like it is doing. manual brake MC's must have that recess. power brake MC's can function with or with out the recess cuz they are setup different & as you know you want the right piston bore diameter for your app. EDIT Rick Ehrenberg iirc used silicone to lock it in there which I thought would be risky but Eberg has forgotten more info than I know so I would be OK with that as a solution.

I had that happen on my old drag Duster at LACR, luckily the shut down area was up hill and the track was long I ended up using some plumber tape on the pedal mounting brakets to make sure that would happen again
I had replace that master cylinder and omitted the retaining ring
I'm lucky I survived that deal without hurting me or the car

In some installations the brake light switch will prevent the pushrod from backing out; looks like yours is missing.

Fabricate a bracket to act as a pedal up stop.

yes I will fabricate something

The car is a procharged bb so its getting quicker and I could get into problems fast

I was wondering if I'd have that problem in my '55 Plymouth given that there's no groove on the pushrod to hold a rubber ring. But, it seems to stay in just fine.

The '55 has a positive pedal up stop...the BL switch is on the master cylinder.