Why when applying MMF to my cakes it keeps getting sticky no matter what I do

Reasons might be that you covered a chilled cake with mmf or that you rolled it out in icing sugar.

I don't cover cakes in fondant...I'm a believe in buttercream.  But I do use fondant for lots of accent work.  The couple times I make MMF and used it the longer it set the more it melted.  I never tried it on a cake that I sold, just a couple for the family to eat....but quickly learned it doesn't work well for me.

That happened to me recently. I was sleepy when making it and didn't realize I forgot to add the last cup of confectioners sugar. Also, the recipe I have says I should let it rest for 24 hours. Not sure the recipe you are using, but maybe add more sugar or let it rest if you just made it.

 If it gets sticky while applying it to the cake, could be it's very humid or your cake is chilled.  I always have this issue when I'm covering a SMBC cake because it's well chilled.  I just dust it with powdered sugar so I can use my fondant smoothers without them sticking to the cake.  No big deal.  When I'm done, I use a pastry brush to remove the excess sugar.

When the cake eventually comes to room temp, the fondant dries.  Try that and see if it helps.  I promise, dusting it with the powdered sugar will not hurt your mmf.