I don't do anything until the leaves have died down, then cut them and leave corms in the ground and they will get bigger and produce baby corms every year.

You don't say where you live. If you are in the north I would dig them up. Further south they should be OK as Cammomile says.

I grew some gladioli this year and was disappointed with them. Those that flowered (5 out of 12 wine'n'roses) only lasted in bloom for a few days (probably only a week) and the others (Prince Claus?) haven't put out any flower buds at all). As I was always told to treat gladioli as annuals I won't be bothering with them again. Maybe I just had them in the wrong compost/wrong place but I opted for glads as I knew I didn't have the sun for bearded iris.