Automatic Shifting Hard

This sounds like a mount. They are fluid filled, so check if you get any oil like substance on any of the motor mounts, if you do see it, replace that one.
Or just buy a pack of 3 on-line and swap them out, not a very hard job, just some wrenching.

I mentioned this in another thread, but no one responded yet. Will 2010 mounts fit on the 2012?
 
update:

Ive now got 120,000 miles on my 2012 Mazda5. The automatic transmission still shifts extremely hard when downshifting into 2nd gear under a load. Sometimes it still hangs up in a higher gear when I almost roll to a stop and then need to accelerate. When I press the gas I get nothing until it slams into first.

I have changed the transmission fluid again and installed a new set of shift solenoids. I also installed a new set of motor mounts. I inspected the transmission mount and found it to be in good shape.

Im still at a loss for how to keep the transmission from downshifting so hard. The Mazda dealer that is an hour away wants $150 to run a diagnostic plus whatever repairs are needed. Any more ideas?
 
How many total drain/fills have you done since you got the car?

I have done two. I did a full flush at 75,000 miles and a drain and fill at 100,000 miles. I’m planning another one for 125,000. I just figured it’s cheap insurance to keep fairly fresh fluid in it. It can’t hurt, right? Oh, and I changed the filter both times.

I just can’t figure out why the downshifts just don’t work right.
 
I have done two. I did a full flush at 75,000 miles and a drain and fill at 100,000 miles. I’m planning another one for 125,000. I just figured it’s cheap insurance to keep fairly fresh fluid in it. It can’t hurt, right? Oh, and I changed the filter both times.

I just can’t figure out why the downshifts just don’t work right.

And have you only tried transmax?
 

I'm driving with the older 4 speed auto so this isn't apples to apples, but I can say with certainty that mine has much smoother shifts after it warms up. Meaning my tranny likes thinner viscosity ATF. And I've alway run Valvoline MaxLife ATF at more frequent drain/fills than you have been doing. And doing some reading I see that MaxLife is thinner than TransMax at all temps. So if your tranny is like mine and likes thinner ATF, you don't have much to lose by doing a flush with MaxLife and seeing if that improves anything.
 
I have done two. I did a full flush at 75,000 miles and a drain and fill at 100,000 miles. I’m planning another one for 125,000. I just figured it’s cheap insurance to keep fairly fresh fluid in it. It can’t hurt, right? Oh, and I changed the filter both times.

I just can’t figure out why the downshifts just don’t work right.
Just doesn't make sense. I own my 2012 since new. 95K miles. Did trans twice. Once at 66k and once at 89K. Trans is perfect since day one. I mean it ain't no Lexus, but isn't hard shifting. I live on top of huge hill, so I go up the hill 2nd gear, and come down 1-2 gear too so my trans see a lot of shifting and holding gear.
 
I'm afraid the issue may not be due to something fluid-related. In my 2014 (same powertrain as 2012, really), the ATF was replaced via the drain-and-fill method once at 33k miles and one other time at 50k miles. I'm at 61k now and will probably do another drain at 65k miles. I used Castrol's Transmax fluid market Import Multi-Vehicle on the bottle both times. The PDS of this ATF states that it is compatible with this A/T unit. I haven't noticed any change in shifting after all of this service so all good. Wish I could be of more help.

I will second what ttwheelsquad pointed out re: viscosity. Per PDS of MaxLife, its "thinner than the "thicker" Transmax. However, both should work in this transmission. At the same time, temps where I live are often below to well below freezing between November and April. The transmission with the current fill of mostly Transmax is a bit slow to shift when cold but warms up fairly quickly and overall does fine shifting up and down. I don't remember factory fill being noticeably better.
 
Back