If you suspect your Faction is specifically being worked against by failed Missions or other direct negative Actions that don't leave visible traces in the Crime Report (Negative Trade, Smuggling), make sure you check the System's Influence distribution after each tick and de-normalize it.
Once you de-normalize the new numbers, you can estimate how much direct work was done against your Faction and what level of positive Support other Factions received.
It's not perfect science but usually works very well.
If you're getting hit directly (negative Inf vs. your Faction), you'll see a rather even re-distribution of your lost Influence. Yours went down, got distributed to all other Factions and these rise proportionally to their total Inf from the previous cycle/tick.
With experience (and any pocket calculator or spreadsheet matrix), you can identify and potentially benchmark the Intensity of the -Inf attacks. Plotted over a longer time, you might even be able to predict it and run a successful preemptive counter.
When correlated with Traffic Stats of Ship Traffic, it's sometimes even possible to isolate individual Ships/Ship types (requires tracking of own Traffic and obviously is best applied to limited Traffic Systems, naturally tends to stop working when traffic and traffic diversity exceeds certain thresholds).
It's very tedious, but at least in less frequented areas of space with limited Traffic, it's technically possible to track such traffic over time and identify its most likely own base of Operations. Even a Solo Mode runner.
Doing so involves alot of time and effort though, as this means running full Traffic Analysis every 24hrs on many Systems. Once you have isolated Ship type(s), the correlation with adjacent Sectors can begin. You're doing Traffic Forensics. Very tedious!
I didn't do that often, but I was able to reliably track down Solo runners that were operating as a small Group out of a 50-60LY distance. Was totally worth it though, as it finally produced the needed Targets for full-scale CI Operations
(which was a smashing (pun) success - they felt totally safe and never saw it coming... fun times)
Anyway, I always found above techniques extremely useful, especially when i.e. other Groups or Players from them made claims about "Who's doing it" or just really checking "What really happened there in the 1st place".
Already prevented alot of conflicts and usually permitted a much more effective defense (within given BGS limitations that is) - sometimes even allowed to give back some love.
The usual disclaimer : nothing described above can do magic, but it's worth a shot if the local environment is suitable for its application.