I replaced the sink sprayer nozzle on my kitchen sink about 3 months ago and it seemed to be working OK (with the exception of less water pressure than before it broke). Then, one day the nozzle popped right off when my son turned on the faucet (Moen single lever). Water comes out of the hose, but not out of the faucet. If I hold my finger over the hose, water will come out of the faucet. Of course, I tried to screw the nozzle back on, but unless I hold down the nozzle lever when I turn the water on, it just pops off again. What would you suggest?

speedball1

The sprayer's pressurized whenever the faucet's turned on. Normally,with the sprayer head connected and turned off the water comes out the spout. When you turn the sprayer on a diverter snaps shut and shuts the spout off.
Unless you've stripped the threads the sprayer head should thread on tight.
You might wish to purchasea new hose and sprayer and connect it back under the faucet. There's nothing wrong with your faucet. I have Moen throughout my home and my company installs Moen in all its up scale new construction. This is a faucet that I'm personally sold on. Cheers, Tom