What makes this capacitor get hot?

I am using a 12 volt 5W solar panel to drive a Microchip MCP73213 dual cell LiPo charger chip.

To keep the Solar panel voltage down to the workable range of the MCP73213 (4.2 to 13 volts) I have put a 5W 12 volt zenner across the input terminals of the MCP73213.

At any thing other than bright sun the charger would not charge even though the input voltage, measured with a multimeter, was around 10 volts (well within the working range of the chip). However, when I put an electrolytic 1000uF 25v capacitor also across the input of the chip, the charger seemed to work fine for a while.

The only problem is that I noticed the charge dropping off and started checking the circuit. The capacitor was too hot to touch and the end was starting to bulge. I disconnected the solar panel and let it cool. I then connected it again and it seems to be fine now. I don't want it to cause problems in the field. The zenner and demands of the charger keeps the voltage below 12 volts (half the rating of the cap).

Why would it be overheating?

It's faulty, replace it.

You want a small value capacitor on input and output, 1uF minimum, it can be unstable without these capacitors.

Sounds like the capacitor was faulty or you connected it the wrong way round (explosion hazard, note).

Solar panels are not very good voltage sources, note, so a larger value input capacitor might be a good idea, but start with 1uF at both input and output and see if that works.

In low light the panel will not be able to produce as much current, I'm not sure that chip will behave when that happens - it may be that the chip pulls current from the capacitor, the chip shuts off, capacitor recharges and the cycle repeats. This will cause ripple-current into the capacitor, suggesting a high ripple-current rated input capacitor is required - this might be why yours failed.