I can't win on planetary fights other than the first tutorial. Can someone help with this?

For most battles works this tactic:
3 robots with 4 rocket launchers+locators hold the line
2 robots with 4 repairs+speed up repair them from behind
Hold chokepoints, after destroying wave capture next plant and wait for new wave.
For most maps 2 groups are enough, third can be mobile capturers.
Eventually AI would be out of resources (he would start to use robots like machinegun on legs) then capture his base.

Is it Jawaiian Islands?
There is one mission that is notoriously difficult but I'm not sure the name. It got to the point I just made sure to skip it every time it was offered.

Kind of a late response but I have had some luck recently.

The big thing to know is that your robots are DUMB and group movement is Terrible. Because so many weapons have AOE effects keeping your robots positioned correctly is key. Robots have an interesting feature where they will try to move out of the way of friendly robots trying to reach a position, after the robot passes by they will return to their starting position. When you move robots as a group they get all tangled up trying to get out of each others way. when trying to set up a defensive line you have to move each robot individually.

If your having trouble getting robots to capture bases give them the Capture base program from the side menu.
Also Bombs are a great equalizer, not for you though, you won't be able to micromanage well enough. but pay close attention to enemy units with back modules, one well placed bomb can wreck an entire robot supply. Also anything that explodes does damage to nearby robots so wait for the carcasses to stop smoking before advancing.

Because of the unit cap it is always better to make more powerful robots than cheap ones. except in the rare case when you can pull off a bomb.

If you need a breath to think or to re-position the camera hit escape to pause the game and look around.