Mercury Grand Marqui 2000. Had issue last winter with needing to be jumped on very cold days. Was fine in summer. This winter the problem returned so I bought a new battery. Still, when car sits for more than a few hours I have a portable jumper I have to use. Except last week one time I shut the car off right after a jump (accident) and it would not re-start, even with jump cables left on 8 hours until the flashing light indicated battery was full. Would not start. Next morning hooked up the jump kit and it started. It's been starting up with a jump every few days but today I jumped it, drove for 20 min and let it sit for 2 hours and it would not take a jump from a truck. Put gas in it, that isn't the problem. Lights work, car cranks it just doesn't ignite. Usually with the 4amp charger it will start in 2 minutes even after sitting for 2 days. But tonight it would not start same as last week. Like it will only allow 1 jump per day? So it does jump most of the time, crank sounds normal, no clicking, no issues with lights while driving or misfires, no other symptoms. I thought 100% it was some drain but the fact that it isn't taking a jump tonight must mean something else is going on?
From our discussion in the comments, it would appear to me that you possibly have a bad connection of one of the wires on the battery positive post. The starter is getting power, but maybe one of the other wires that gives power to the ignition or fuel pump is not connecting every time. I think adding the jump connectors you are making the connection work.
I would remove each of the wires on the battery terminals and check and clean them before refitting them.