I frequently use the M1-M4.
Since setting all the 16 available macros to be used along the kpod the M1-M4 Auto-Repeat is not working anymore.
what I have done:

I cleared M1-M4.
I cleared bank1  and bank 2.
loaded a backup K3 config.
I cleared all the macros set from 1-16. wrote them to the K3.
Tested M1-M4 Auto-Repeat with the k-pod disconnected.
Recorded a short and long message to repeat.
I tested M1, M2, M3, M4 thinking it maybe a button, all of them do not auto-repeat.

Holding M1-M4 shows REPEAT briefly on the VFO/B then goes away quickly and the loop icon above the S-Meter is no longer there.

I remember in the programmer's guide says the M1-M4 were part of the programmable functions but I cleared them all and the problem still persists.

any suggestions?

Others can chime in about the procedures you mention, but I can tell you it may need firmware (FW) updating.
Go into config menu, the default that comes on when you power-on is "FW REVS",
Rotate VFO A clockwise to "dr 0x.xx";
If you have 01.04 or less you are OK (old rev board).
We had to goto different chips on the newer board and went to FW 02.xx
If you have 02.xx that is less that 02.05, you need to send it in for updating.
The board has to be taken out of the radio, so you can send in just the board.
If you have an older radio, it may be best to send the whole radio so I can do all the updates.
What is your serial# ?
Do you know if it has had any updates done?
Keith WE6R Elecraft K3\K4 Tech

SN(5793)
K3 KDVR3
K3 KXV3B
K3 KIO3B USB
MCU 05.67
FPF 01.26
DSP1 02.88
DSP2 N/A
DVR 01.03

You are OK on the DVR FW 1.03, it did not have any issues.
Someone that uses on extensively should be able to help you.
I do remember trying to do auto-repeat once and I could not figure it out.

Your serial # already has the front panel gold pins, (which is an important update).
So nothing too serious as far as the rest of the updates.
Keith WE6R

More troubleshooting data:

• I performed a EE INIT.
• Restored my config using the app.
• Recorded a new message
• The memory auto-repeat started to work again in TEST MODE.
• Switched to NORMAL TX.  auto-repeat worked once, I stopped, tested again and stopped working again. When the M# button is held, VFO/B shows REPEAT then it goes away. When it works REPEAT stays in VFO/B.
• I did an EE INIT Again to confirm the behavior but it didn't work the second time.