Game Version 7.50 (553255)
No modifications, All DLCs active.
The core issue is receiving the "Lost reputation temporarily" when totally unexpected, and in some cases, when seemingly impossible. I have had this exact same issue maybe only a dozen times over 6,100 hours of game time, but never in such close succession - four issues in 23 in-game minutes. It seems that something odd has happened in my game. Two unmodified saves are provided (plus an image with some combined screen grabs of the ticker events, for what it's worth!)
Most recent save (Balaur):
https://1drv.ms/u/c/79ce8746c389ffcf/ER ... A?e=BFC2fg
In-game runtime: 9Days 17Hours 30Mins - nearly 240 hours in to this playthrough
ANT Rep: +27
ARG Rep: +26
Older Save (Elite and Behemoth):
https://1drv.ms/u/c/79ce8746c389ffcf/ER ... Q?e=B8UAcB
Ticker page of Logbook (as captured in most recent save) shows:
Lost reputation temporarily: - -57
ANT Delivery Ship Balaur
Current reputation: -30
0m ago
Lost reputation temporarily: - -58
ARG Drone Carrier Cerberus Vanguard
Current reputation: -30
17m ago
Lost reputation temporarily: - -58
ARG Fighter Squadron Elite Vanguard
Reason: Unauthorised Attack
Current reputation: -30
21m ago
Lost reputation temporarily: - -58
ARG Patrol Destroyer Behemoth E
Current reputation: -30
23m ago
I also captured three of these four entries via screen grab at the time, combined in to a single image, oldest (top) to newest (bottom):
https://1drv.ms/i/c/79ce8746c389ffcf/Eb ... A?e=plcRrC
The most recent of the two save games was taken just after the ANT Balaur message appeared (presumably a FRF or FAF pirate ship running the ANT identity). I paused and checked in the map and could not find a ship matching that name in any visible parts of the map, despite a fair bit of Adv. Satellite coverage. No idea where this ship is, and why I've lost rep with it. No reason is given.
The previous incident was the ARG Cerberus and I paused and looked for a suitable ship with that name and was hostile - nothing. I unpaused and did eventually find that ship as it flew north in to range of an Adv Satellite placed at the east end of Hatikvah's Choice I where there was a Xenon incursion happening. The ship was eventually destroyed by the K that was shooting the place up. No idea why I lost rep with this, again no reason given.
The next incident back is the ARG Elite Vanguard. A reason of unauthorised attack was given, however there was no attack. I was onboard the Cobra which had just deployed an Adv Satellite at the west side of Morning Star III and was about to deploy another one towards the east gate. When I saw the message, I paused and saved - this is the first of the saves. Very close to the Cobra was an ARG fleet comprised of Fighter Squadron Eclipse Vanguard (PRC-775) with two subordinates Fighter Squadron Elite Vanguards (with IDs NLX-448 and QBY-447). I suspect one of these two Elites was the one mentioned in the ticker message, as all three turned hostile (red in the map) immediately. I had to take control of the Cobra, disable the turrets, and fly out of the east gate and dock at the HAT trading station to prevent escalation. Subsequently those three (still hostile) ships flew throught the west gate to Heretic's End (under my control) and are still patrolling there. Again, no attack took place as the only ship capable of this I was on board as a passenger, and it was deploying Adv Sats.
The oldest one showing up in the log is the ARG Behemoth (almost certainly ID VWE-046) which I first spotted *after* the Elite Vanguard issue above, and I saw it heading south west towards the west gate in Morning Star III and, like the Eclipse and two Elites, started patrolling in Heretic's End. The Behemoth was hostile (red in the map) however none of the accompanying fleet (3 M ships and 12 S ships) were. Again, no reason was given.
With two separate ARG fleets each with one or more hostiles flying around Heretics End in which I have the HQ and the bulk of my ships that are not currently in use, I undocked the Katana (granted from the Terran Yaki plot) from the HQ which was still located there, and flew over to each fleet (they were hundreds of Kms apart) and then engaged the cover to YAK, waited for them to notice, then disabled it again. This cleared the hostile status, thankfully, as both those fleets remain patrolling around "my" sector now.
The whole time I've been mindful of ensuring that my ship's captains don't have any controlled inventory items, and they don't touch the contraband cargo like spaceweed etc., so I believe it's highly doubtful that this is the cause to about 99% certainty.
I found it very strange that these events have happened in such short succession. The two oldest issues (the Elite and Behemoth) had two precutionary reloads afterwards just after the older save had been taken - this was all yesterday, and the game was shut down. Today I launched the game hoping the problem was gone, and the most recent incident (the Balaur) happened, suggesting that whatever this issue is has persisted through multiple save/reloads and at least one game re-launch. I suspect after nearly 240 hours this save cannot be resonably continued, which is a bit frustrating.

Some other suggestions that could assist tracking down (normally) uncommon issues like this - When showing (and logging) the "Lost reputation temporarily" message:
1. It would be extremely helpful to show the ship/station ID as well as the name, to prevent any confusion.
Bonus points for storing the location where the incident took place, as with other log entries.
2. There should *always* be a reason given, for avoidance of doubt.
Three of the four messages I highlighted above had no reason given (and the fourth did give a reason, but the incident never occurred)
3. It would also be helpful to have this message written to the General part of the Logbook where other Reputation related messages appear - the Ticker section of the Logbook doesn't seem to keep nearly as much history.
I know this probably isn't that much to go on, but hope that having two saves helps. Of course these game world events have a level of pseudo-randomness to them, but lightning has struck four times in a row with this playthrough, so there has to be something up!

Off to start a new save...