Brita faucet filter will not stay on faucet

Want a free adapter and patient enough to wait for a couple of weeks to get them?
"To receive a special adapter free of charge, call 1-800-24-BRITA or 1-800-387-6940 (CANADA)."
Call the number above and a voice prompt will give you instructions on how to get your adapter for free. 2 weeks might be too long but the best thing is it is made of stainless steel/chrome and it comes in 3 different kind of adapters with rubber washers.

I had the same problem and struggled with various solutions including silicone glue and removing the screen. Silicone glue doesn't really hold and I believe the screen is needed to aerate the water prior to filtration.

At any rate, I finally fixed this by going to Home Depot and buying a METAL adapter as opposed to the provided plastic one.
"Bubble-Stream" Faucet Adaptor
15/16" x 55/64" -27 [It looks EXACTLY like the plastic one provided only its metal] for $3.86

and an assorted O ring package
Danco Stem Repair Part #80384 for $0.78

So under 5 bucks with tax out the door.

Threw the plastic adapter out the window, put the washer and new metal one on the faucet.

Cut and pulled apart the screen/white washer in order to get to just the screen.
Put the Danco flat washer collar in the Brita
Then the screen
Then a Danco O ring washer on top.

Screwed in the Brita.
Very slight, livable dribble on fitting, but the system is fully function and stays on now.

Thinking of putting some silicone glue on the Brita threads to fix the dribble at some point in the future but for now I'm satisfied.

Hope this helps

I also had this problem where my Brita on tap filter would fall off with the slightest touch. With our faucet, no adapter was needed. As others have mentioned, the problem is that with the white washer/mesh dome assembly in place, there is not enough additional threading to secure the unit to the faucet under pressure.
My solution was to do the following:
1) Remove the white washer/ mesh dome assmebly and pry the washer away from the mesh...keep the mesh.
2) Go to Lowes, Ace, or any hardware store and get some teflon valve packing string, like this from Lowes - http://preview.tinyurl.com/27g55pu. I had some on hand after repairing an outdoor spigot. This stuff compresses a great deal and forms an amazing seal.
3) Lay the teflon string inside the water filter where the old washer was. Mark where it overlaps and cut it. Sort of pack it in and flatten it out a bit with a flathead screwdriver, especially where it overlaps.
4) Place the mesh dome on top of your new, low profile washer. Wrap some regular teflon tape around the threads of your faucet and re-attach the filter.
That should do it. The teflon washer will compress far more than the original rubber one, allowing more thread to grab onto the faucet and creating a rock solid connection. The teflon tap on the faucet will prevent any leakage that might occur at the point where your make-shift washer overlaps.
Hope this helps someone out! Thanks...

Before I address the issue, here was what I experienced: (1) there is not enough threading on the adapter (2) the whole thing was leaking. My solution: I went to the hardware store and bought a metal adapter. I used the rubber washer that came with the Brita adapter AND I used a 2nd rubber washer (the one that was originally on my faucet). One rubber washer fits in with the metal adapter just like it fitted the plastic adapter. I stack the 2nd rubber washer above the 1st one (NOTE - just stack it. DO NOT try to stuff the 2nd ring into the adapter). Insert the 2 rubber rings/adapter assembly into the faucet head, then screw the adapter in. With the 2nd rubber ring, you have now made available more threading for the Brita to attach to. And you have reinforced the faucet from leakage. Now, screw on the Brita. Voila! No leaking, no fly-away Brita, no additional tape, no glue, no wire.

Here's a little hack that worked for me:
I noticed that the aerator/washer that comes with the filter was blocking the adapter from going far enough in for the threads to really take hold. So, I removed the aerator from the filter connection and moved it to where the black washer is supposed to go on the adapter (i.e., the dome-shaped aerator ends up in the faucet head when you screw in the adapter). I also wrapped thread tape (teflon tape) around the filter-end of the adapter to create the seal that would have otherwise been taken care of by the washer attached to the aerator. I needed to layer the tape on rather thick, but it seemed to work pretty well. No leakage/dripping so far!
Of course, I only did this because I had thread tape on hand...if you have to go to the hardware store anyway, it might make more sense to just get a metal replacement adapter (or have Brita send one to you for free if you're patient enough).

As Bryan Coolit mentioned in Solution 2, you can get a stainless steel adapters from Brita for free. I called and talked to someone instead of going through the voice prompts and I don't know if that made a difference, but it only took about 4 days for me to get the adapters. The adapter I used works very well and the faucet filter doesn't fall off anymore. I suggest calling them!

Brita's replacement adapter is backordered for many weeks.
Home Depot-Neoperl faucet adapter 571493
easy on, no leaks, frustration and getting soaked everytime the Brita fell off is OVER!!!

True, using the 'new' plastic adapter is unreliable. it may work for some models of faucets, but not for others. if you bought a replacement, and you have the old metal adapter, use that one. clean it up with vinegar to remove the calcium deposits use the new wire mesh filter and rubber gaskets and install. it works fine.

Not a solution, but more info

I got a new Brita that will not stay on. It will not stay on the faucet that used to work with our old Brita, and it will not stay on the adaptor that Brita sent out. The threads on teh new one seem to be rounded in comparison with the old threads, and I measured the inside of the collar on the Brita, the old one is 82 hundredths o fan inch wide, but the new one is 83 hundredths. Somehow it's made differently and that is why it won't fit and we are trying all these ways to make it work!!