Routing convex on ends and one edge of same board

End grain 1st...

Sounds like you're not going to do anything with the 2nd face...

If that is the case you might want to do a small climb cut on the 2nd end grain cut as you won't have the 2nd face to clean it up. If so, do the climb cut on the corner of the 2nd end grain cut that is away from the face you will cut.

So if your board is standing up and down with the end grains at North and South and the face to be cut at West, cut North first, then West, then climb the Southeast corner, then cut South. The entire direction would be counterclockwise except for the climb cut. (assuming handheld)

If I got it wrong, then do exactly what Stick said...end grain first, long face, end grain, long face last.

What profile are you cutting and are you cutting freehand or table...?

Sorry, I should have explained a bit more.
I am working on the mission mantle clock from Klockit. The top plate and bottom plate have convex profiles on the ends and front- 3 edges of the 4 need this convex. The back does not. Just on one face of each board. I am attempting to do this on my router table with a Bosch 1617evs router. Thanks for your help.
Bob

route the end grain 1st using a sacrificial board to avois tear out...

.

Or use a push block to push the board past the bit as shown in this video at the 5 minute mark: https://www.youtube.com/watch?reload=9&v=hHnLvps8968

I usually just grab a leftover piece of ply or mdf that's from 6-10 inches square and use it to push my work through. That keeps it square and and reduces the chance of blowout to near zero. Clamping the board to your work is about 99%+ foolproof.

Thanks for your help. I got it done with a sacrificial push block like you suggested. It worked out great.