Transmission problem? Once the car has been driven for a period of time the transmission will go into 2nd gear on slowing down and will not move. I can't shift up or down. The car needs to be turned off and restarted. This doesn't happen when the car is first started.

Question edited for clarity.
Question moved to year model category.

Check the Automatic Transmission level, but you may have solenoids that are failing.

It has known transmission issues.

https://www.google.com/search?q=2006+Mazda+3.+The+transmission+goes+into+2nd+gear+when+I+start+in+the+mornings

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This is often times a sign of low transmission fluid or a faulty transmission control solenoid. As you know, automatic transmissions use pressurized hydraulic fluid to change gears or to stop showing 2nd

check replace engine and transmission mounts

Do you notice that this happens after a common pattern. For instance after you have driven for a long period of time or only when you are accelerating faster than normal like peeling out?

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Could be a worn synchromesh on the second gear.
Maybe if you practice double de-clutching it will delay the necessary strip-down. The other technique is to monitor the revs during change up to see what the optimum engine speed is for a good silent gear change

This is a fault mode in which the transmission either loses electrical power or the PCM deactivates all of the electronics. The transmission will default to max line pressure. The driver will have Reverse and 3rd, with manual 2nd available by putting the gearshift in 2 or 1 (doesn't matter). 1st, 4th, and TCC lockup will not be available. It will not hurt the car to drive it like this for short periods, but use manual 2nd to get the car moving, and be aware that the trans will generate more heat than normal while operating in limp-home mode due to increased torque converter slippage during 2nd gear starts and no lockup in 3rd gear.

Trans shifts into gear harshly, car feels sluggish off the line, No 1st, 4th or TCC lockup available, Manual 2nd, 3rd and Reverse are only available gears, CEL is on: Transmission is either in limp-home mode or has lost electrical power. If there are lots of error codes in the PCM, check the under hood fuse that powers the transmission, and if it pops again, look for a short in that circuit like an O2 sensor harness touching exhaust. Otherwise, check PCM codes for a particular fault in the transmission causing the PCM to put it in limp-home mode.

No 1st or 4th available; trans shifts 2nd to 3rd by itself in D or OD and locks the converter : ShiftA solenoid failed. Easy fix in the pan. Or a wiring problem from PCM to trans.. or PCM.

Car goes into gear but feels very sluggish like the brakes are dragging, but it will roll easily (starts out in 4th gear), you manually shift to 2 to get it moving, once it's moving you put it back in OD and the car shifts 3rd to 4th on its own and locks the converter at the appropriate time: ShiftB solenoid failed: Easy fix in the pan. Or a wiring problem from PCM to trans.. or PCM.

Your transmission apparently is not downshifting properly. From your description, it sounds as though it is in 2nd or 3rd gear, which is why it is slow to accelerate. When you shift into 1st, it is starting off in 1st gear as it should. You probably should have a transmission shop check it out. Check engine light on?