How firm is this connection?
Tape under the nut isn't the right way to do it.

Read the instructions on your wire nuts they may or may not require that the wires be pre-twisted. I get the ones that don't require pre-twist, line the conductors up so the ends are even, and twist the nut on. Give each individual wire a tug and if any pulls out, start over again.

Sometimes I just can't get the wire nut to twist on and make a tight connection. In that case I line up the ends of the wires and pre-twist them with lineman's pliers. In order to get a good twist I've had to resort to using my needle-nose vice grips across the three wires to hold them in place while I get a twist started with the lineman's pliers (if you do something like this, be careful not to damage the insulation where you grip the wires).

Of course, this all assumes you're using a correctly sized wire nut. Read the instructions on the packaging and there should be a capacity chart for your particular wire nuts.