My suggestion would be to "borrow" some foam from some of your old cut off rubber (every SU person has a zippy bag of left-over rubber from cutting sets!).
Take your scissors and cut the foam from the back of the rubber of the flower stem (make a nice, neat straight cut - nothing fancy). Find a piece of old rubber with foam that is larger than the stem - heat the old rubber in the microwave for a few seconds to soften the glue and then remove the foam from the old rubber and attach it to the back of the flower stem.
You now have new foam on the back of your stamp that "butts up" to the old foam. Now trim the foam around the rubber - just don't trim it as closely as you did before
I have found that if you trim the foam on a slant (foam is wider where is attaches to the wood and narrower as it approaches the rubber), it makes for more stable rubber on those skinny parts like stems...the point of trimming the foam on a slant is that it won't pick up any ink when you stamp, but it still will provide stability for the rubber.
Hope this makes sense!
Susy