I use a 13" MacBook Air M4 running MacOS 27.0.1. In September I bought a 2TB SSD disk to act as a back-up disk. I formatted the disk as APFS and completed (as I thought) my first back-up. It all seemed to work correctly as I found a back-up file on the disk and I tested the result by using Time Machine to recover a small file without any difficulty. I carried out 10 manual back-ups over the following few weeks and all seemed to be well, each backup showing up on the back-up disk as I expected.
A few days ago I needed to recover a file from my back-up disk. When I entered Time Machine it showed the file but only showed back-ups for "today" and "yesterday" despite the file having been in existence since well before my first back-up on 8 September. (Luckily, the "yesterday" version of the file was able to fix my problem.) The lack of access to any other, older, back-ups prompted me look at a bit more closely at Time Machine and I was surprised to see that, in its Settings it displayed the message "Waiting to complete first back-up". It has been waiting since 8 September. I also noticed that a back-up which I did today showed "Back-up failed" in the dialogue. (As an aside, having found the problem I was surprised that Time Machine does not flag up the problem of a failed back-up as it occurrs, or have I missed it?). Attached is a screenshot of the Time Machine's Settings.
This has shaken my confidence in the integrity of my back-ups and I would be grateful for any suggestions about how to overcome the problem.