You are possibly using the wrong size wirenut for the number and size of wires you are connecting, or simply installing them incorrectly.

"Saving money" is a dubious justification for tackling electrical work if you are not up to the task - the money you "save" can easily cost you a good deal more when your work fails in a more dramatic fashion and burns the house down or injures/kills someone. You could hire an electrician to go over your self-installed wiring and make sure it was correct, and odds are excellent that no more wirenuts would fall off after that.

There are "push-in" wire connector blocks made and listed now. I'm not personally a fan of them, but they are made and listed.

i.e. this image from Ideal industries (not endorsing or associated, just using the image as an example:)

You are possibly using the wrong size wirenut for the number and size of wires you are connecting, or simply installing them incorrectly.

"Saving money" is a dubious justification for tackling electrical work if you are not up to the task - the money you "save" can easily cost you a good deal more when your work fails in a more dramatic fashion and burns the house down or injures/kills someone. You could hire an electrician to go over your self-installed wiring and make sure it was correct, and odds are excellent that no more wirenuts would fall off after that.

There are "push-in" wire connector blocks made and listed now. I'm not personally a fan of them, but they are made and listed.

i.e. See this image from Ideal Industries (not endorsing or associated, just using the image as an example) 

You are possibly using the wrong size wirenut for the number and size of wires you are connecting, or simply installing them incorrectly.

"Saving money" is a dubious justification for tackling electrical work if you are not up to the task - the money you "save" can easily cost you a good deal more when your work fails in a more dramatic fashion and burns the house down or injures/kills someone.

There are "push-in" wire connector blocks made and listed now. I'm not personally a fan of them, but they are made and listed.

i.e. this image from ideal industres (not endorsing or associated, just using the image:)

You are possibly using the wrong size wirenut for the number and size of wires you are connecting, or simply installing them incorrectly.

"Saving money" is a dubious justification for tackling electrical work if you are not up to the task - the money you "save" can easily cost you a good deal more when your work fails in a more dramatic fashion and burns the house down or injures/kills someone. You could hire an electrician to go over your self-installed wiring and make sure it was correct, and odds are excellent that no more wirenuts would fall off after that.

There are "push-in" wire connector blocks made and listed now. I'm not personally a fan of them, but they are made and listed.

i.e. this image from Ideal industries (not endorsing or associated, just using the image as an example:)