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I cannot tell what is the reason that the trackpad gestures stop working but here are the symptoms:

• Trackpad gestures would be working fine. For instance: smart zoom (double finger tap) or Swipe with two fingers to go to the previous page


• After a while, Safari stops reacting to those gestures. Even If I try to close and kill all Safari instances, I still get this problem. The solution is to reboot then those gestures work again.

Did anyone face this problem? How to resolve it?

EDIT 14_1204: It's a Safari bug. Disabling extensions seemed to work, but it started again. It only seems to affect Safari and App Store, so it's probably related to the swipe animation handling in those apps.

EDIT 14_1129: After a few days, the problem came back for me. Resetting PRAM is apparantly working for other people, but in my case, I suspect it was interference from a Safari Extension. I haven't narrowed it down exactly, yet, but I only had four extensions which could've been the culprit.

1. No More iTunes


2. Instapaper


3. Reddit Enhancement Suite


4. Evernote Web Clipper

After disabling (but not uninstalling) all extensions and restarting my Mac, gestures seem to be back at 100% for a good while now. Still, I can't say for sure that extensions were the issue. The issue also cropped up with the Mac App Store before the fix, and I'm not sure what to take from that.

Original Answer:
Resetting PRAM worked for me. Apple's instructions page for resetting PRAM is unavailable at the moment, but plenty of sites have reposted them. From ihash.eu:

1. 
   Shut down your Mac.


2. Locate the following keys on the keyboard: Option, Command (⌘), P,
   and R. You will need to hold these keys down simultaneously in step
   4.pram reset graphic How To Reset Macs PRAM in OS X 10.10 Yosemite


3. 
   Turn on your Mac.


4. 
   Immediately press and hold the Option-Command-P-R keys. You must
   press this key combination before the gray screen appears.Continue
   holding the keys down until your Mac restarts, and you hear the
   startup sound for the second time.


5. 
   Release the keys.

Words of Caution:

If you have a Redundant Array of Independent Disks (RAID) scheme set
up, your computer may not start up if you reset parameter
random-access memory (PRAM) when you restart.

If this happens, hold down the Option key while you restart your
computer. Then select your startup disk when you see the prompt. After
you successfully start up your computer, choose Apple menu > System
Preferences, click Startup Disk, then select your startup disk.

Resetting PRAM may change some system settings and preferences.
Remember that your chosen startup disk, time zone, and sound volume
are reset to their default values when you zap your PRAM. Use System
Preferences to restore your settings.