Hi, I’m Louie. Sorry you had to wait awhile but I’ll do my best to help.
To make sure I don't miss anything, please give me a minute to review your question.
Have you tried another SD card?
Or try the old SD card with another camera or even a memory card reader / computer?
Appreciate these additional information; very significant.
Since the SD card(s) can then be ruled out, the most likely suspect would then be the T3 itself or more particularly the finger/contacts based on "...will save sometimes but not all the time..."
Would you be comfortable attempting to check/clean these memory contacts of the camera through the card slot?
Can you try carefully cleaning these contacts?
Consider using a flattened foam swab lightly dipped in plastic safe / non-staining CRC 2-26, DeoxIT DN5 or LPS 03116 Contact Cleaner or equivalent. Allow sufficient air drying time.
In some instances, tweezers may be needed to cautiously re-align these fingers/contacts.
Yes please. Kindly ensure, camera is OFF and batteries removed.
And would look forward to an update.