Hi,
Normally you would make it up in say a 500 ml brown bottle that you can cap and store for a while. Normally as you said you dip your TLC plate in and remove carefully allowing any excess to drip off. The you heat your plate gently with a heat gun and your product spots should appear. It's a nice standard reagent and smells quite sweet too which helps.
Now if you say your silica is falling off it sounds like you have rubbish plates. I hope your not like an undergraduate and the plates are home made cause I remember those days and the silica didn't set well.
Normally I use glass backed or preferably aluminium backed plates that we buy in from a supplier and these pose no problem.
How much c.H2SO4 have you used? You dont need a bucket load.
R.