How do I keep beaters in mixer without them falling out?

Very Carefully! Generally, depending on the make and model there are two small ejection buttons near the beaters portion. Press HARD to make the inside locks disengage the beaters and they will fall out.

wild guess turn beater as you push in to allow the beater to engage the drive, a little like gears meshing. You should be able to feel it lock into the drive.

They need to be replaced or the locking mechanism does, but in the meantime, wind some thread around the beater end and this may keep them in temporarily.

winf=d a bit of thread around the shafts until you can get new ones.

I can't find a manual for the MX55 online, Suzanne, but looking at the picture of it I found on Amazon and based on the manuals for other B&D models, it looks like you should have two slightly different beaters: one with a collar and one without and it's very important that each beater go into the correct hole. The one with the collar should go into the left hole (looking at the bottom with the holes at the top) and the one without a collar into the right. The other manuals say "insert each beater and, if necessary, turn it slightly until it locks into place." I hope this helps. Good luck!

Edward, it sounds like your planetary is starting to separate.Where the center shaft connects to the planetary commonly separates, the pieces are machine pressed together, and can separate, usually your beater, and planetary plate will just fall off into the mixer, while the center shaft stays up inside the mixer with the gears on it.

What you will need to do is buy a new planetary assembly, you do also have the option to have it pressed back together by a machinist, but it is usually cheaper just to buy a new planetary. According to your model number you have a Onyx Black mixer, here is a link to the replacement planetary on our website: http://www.mendingshed.com/9708176.html

That should solve your problem, also here is a link to the service manual in case you need any help taking the mixer apart: http://ep.yimg.com/ty/cdn/mendingshed/kitchenaid6qtservicemanual.pdf

And of course, if you need any help you can call us and speak with a KitchenAid technician over the phone

Thank you,

Colleen
Customer Service
MendingShed.com

The kitchenaid warranty is exactly 365 days from date of registration "No Questions Asked" on day 366 you have no warranty and you gotta pay.
Now the good news; first check the wall socket, I know it works but check it anyway. then check your plug, did you step on it while you were working on the machine? The plug often falls to the floor during work and can get underfoot, you may have broken the plug it'self. next you will need a parts list for your model from Kitchenaid's website.
http://www.kitchenaid.com/customer-service/manuals/
My first suggestion is to try a minor adjustment of the speed control switch, they often get out of sync when you do something to the machine. You can find several videos of this on the youtube site. "Adjusting the speed control switch on kitchenaid mixer"
If the two or one of the top 2 screws on the speed control switch move it can shut the machine down just like an on/off switch. Did you remove the back cover during your adjustments? Did you remove and replace the carbon brushes on the side of the machine while working on the machine? If you did you might have put them back in incorrectly, if you did they will also act a a shutoff switch. If you did not take them out then DON"T as there are four ways to put the brushes back in and only one way is correct and there are two brushes to deal with. Has work ever been performed on the mixer before? Because if all you did was to adjjust the beater height screw then nothing should have effected the normal operation of the mixer. So if there is anything that you did but did not include in your description of work you performed then please let us know. We strive to give accurate solutions but... as I am a KA tech I do not have any other solutions with out the machine in front of me. Just so you know you can fix this yourself.

Repair Kitchenaid Hand Mixer KHM3WH

In taking apart my same beater, I'm trying to figure out the alignment of the spring which provides the tension so that the beaters won't fall out. I'd assume that your spring has mis-aligned. You need to take it apart (3 Philips screws), and carefully pull the assembly apart. I'll bet your spring falls out like mine did. I'm trying to find a schematic from Sunbeam to see how the spring should align.

You need a new gear set.  Hard to find however.