GFCI Outlet in kitchen cutting off power of all other outlets
How to ignore the problem

A GFCI device of any kind, even the kind that looks like a receptacle, is able to provide GFCI protection to other loads beside itself.  It has a couple of output terminals called the LOAD terminals, and anything attached to LOAD will get GFCI protection also.  This is an efficent way to use GFCI devices, but only for people who actually treat electrical maintenance seriously and have a healthy fear of it.  

For others, you get this situation.  

Others are discussing how you can use multiple GFCI+receptacle devices to separate one receptacle's problems from another's, by tactical use of the LOAD terminals (or rather, tactical disuse).  It's straightforward enough; just leave the warning tape on the LOAD terminals and pigtail everything onto LINE.  Once you do that, only things plugged into a GFCI+receptacele can trip that GFCI.   

How to fix the  problem

A GFCI has one job.  What is it? Detecting ground faults: Cases where electrical insulation is not tight anymore, and the appliance is leaking current in a way that could shock you or start a fire.  So if something trips a GFCI, what is most likely to be?  Right.  

One of your appliances has a ground fault. 

This news tends to be disliked.  We've had flame wars with askers who were in full military denial.  If you're not interested in that... 

It is a process of narrowing down.   An appliance may have a ground fault, but it can't trip a GFCI if it's not plugged in.  So unplug all the appliances that have been plugged into those GFCI protected sockets for the last 10 years.  See if the problem goes away.  Once a day, plug one back in and see if the problem returns. 

Here's a useful tidbit: a 2-prong appliance can't trip GFCIs unless it can reach ground somehow - sitting in a puddle of water that often leaks from the sink, a cable modem through the TV cable shield, or a plumbed coffeemaker through the water in the supply pipe.

For a big machine like a refrigerator, run an extension cord to a receptacle on a different circuit, solely for temporarily testing.  Ideally that other circuit is also GFCI, so you get the double confirmation of a) the kitchen stops tripping and b) the other circuit does trip.

Once you find the culprit appliance, you can take a swing at giving it a good clean-up... But realistically, into the trash it goes.  This is an age of throwaway appliances.

Don't be surprised if it's your refrigerator.  That's common, and here's the thing:  Refrigerators don't belong on GFCI.  Refrigerators are the exact opposite of the use-case for GFCI: a grounded machine with all the electrical bits shielded by all metal, in the back bottom where you could not possibly access them, and you aren't going to drop it in your sink.  I have seen cases where the fridge was the last outlet on the kitchen countertop chain, and as a result every single kitchen countertop outlet needed its own GFCI+receptacle, with LOAD terminals not used at all.  If a fridge has a 10ma ground fault, I really do not care.  It's not going to threaten anyone but the ground wire.