I have read a few places that the longer the wire is and the more numerous the outlets hooked up to the load side of a GFCI, the lower the threshold for tripping becomes as a result of leakage current, which may become a problem from frequent tripping. However, I cannot find any hard numbers on the limitations.
Electrical – How many outlets can be wired to the load side of a GFCI
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I'd have to suspect that you are perhaps not always getting the part where the wire actually ends up between the plates right - to Quote @shirlocks answer "Just be sure to tip the device so the grab plates open before inserting the wires." If the wires are in the right place and the screws are tight THIS flavor of back wiring is VERY secure (as distinct from the push in springloaded that I will never use.)
It is generally advantageous to prebend the wires a bit before stuffing into the box, but there's no way the wires should come out if they are clamped correctly.
If the wire is not between the plates (so it's sitting outside them) it's not going to be clamped very well at all. Grab one, (out of the circuit) and look at it carefully under good light with the screws open as you move it around, and you should be able to see what's going on there, and have a better idea of what to look for when putting the wires in.
First, GFCI trips are a fairly quiet snap. The big loud "pop" might actually be a terminal screw arcing against the steel box.
Second, backstab connections (which you jab in and it grabs the wire) are well known to be unreliable, and you're not allowed to use them twice, because the spring is sprung and now they're even more unreliable. How do you keep it straight? Easy, never use backstabs ever.
As far as neutrals and grounds, some folks treat them as if they are mixable and interchangeable. Both amongst each other, and amongst other circuits that may be in the vicinity. It's OK for grounds to intermingle with other grounds, since their one job is safety. However neutrals must not mix with grounds or neutrals from other circuits, because their one job is returning normal current from their partner "hot" wire. They are not fused so they depend on that not to overload. Also, GFCIs depend on this for how they work.
This problem can also show up as a neutral screw rubbing against a ground wire or metal box.
And what can really getcha is an MWBC, two hots sharing a neutral by design. If there's an extra hot in any of your cables, that's what that is. MWBCs are safe if wired corrctly, but do not play nice with GFCIs.
Now I don't know exactly what "as instructed" told you to do. GFCI's have a set of terminals called LOAD, and a novice thinks "sure, they're the second set of terminals like most sockets have". Nuh-uh. They are covered with a piece of tape that says "do not use unless you know what you're doing" in as many words. The LOAD terminals confer GFCI protection to all of the circuit downstream. But if that circuit's wiring has any defects like I discuss above, that will result in instant trip.
The short answer is don't use the LOAD terminals at all. 90% of homeowner use of the LOAD terminals is because their old socket had an extra set of hots and neutrals going to it, and they didn't know what else to do with those wires. That doesn't count as "knowing what you are doing". Not using the LOAD terminals requires a new skill: the pigtail and a few extra supplies.
The long answer is take your wiring all apart and figure out how each cable connects to different boxes. Then come off the LOAD terminals to the next receptacle only, unhooking any wires that go beyond that. Power up and test. If it passes, power down and add the next segment. One at a time. Eventually, adding sometimg will cause it to trip. That is the problem item.
If everything hooks up, then fit everything back in the junction box one device at a time. Power up and test again. This is where you detect screws contacting metal boxes and stuff like that. If you put them all back together at once, and it trips, you'll have no idea why.
Divide and conquer.
If you caught the bolded text above, you now realize that a socket downline of the load terminals of a GFCI is protected by that GFCI. Putting another GFCI there is wasted, it's playing a "yo dawg" joke on yourself. You may also want to rethink whether you want lights GFCI protected, since a GFCI trip will plunge you into the dark with hands inches from a spinning saw blade.
Best Answer
Check the specs with the GFCI manufacturer.
Square D for example has a few requirements for GFCI breakers.
Other than that, there is no restriction per se for how many outlets can be on one branch circuit, residential speaking that is.