You need to convince the bank that any transactions between its being compromised or stolen and your notifying them were not in fact yours. Good luck with that. I would not notice a fraudulent charge until the next monthly statement
I'm not sure where you live, but in the US it's quite easy: most banks allow you to simply mark one or more particular charges as fraudulent using their online banking website. Otherwise, you can report the card as lost/stolen using the website or by calling them. One time, ten years ago, they sent me a form I had to sign and mail back (at their expense) to attest that the charge was fraudulent. Took me about 30 seconds. The one other time I've reported it since then, it was all online with no paperwork. The one time the bank caught it before I did, no paperwork was necessary: they called me, described the suspicious transaction, I confirmed it was fraudulent, and they handled it from there.
There's never been any adversarial questioning or anything from the bank, it's simply routine.
But you sound as if your cards are often compromised, lost or stolen, so it's all the more suprising if your bank cancels the fraudulant charges at the drop of a hat. You must have such a reputation with them that I wonder why they don't cancel your contract instead.
It's happened to me three times in 15 years, never through any fault of my own. I'd hardly consider that "often" or somehow deserving of a "reputation". Even if it was somehow considered excessive, I find it hard to believe that a bank would drop a long-time client simply because they were frequently the victim of crime.
In each case, it's been quite obvious that the charges were unusual and fraudulent: As an example, when my card was compromised one time I lived in Arizona and I regularly made various routine charges (e.g. groceries, gas, food, etc.). It didn't really make sense that my card was used to buy $300 worth of gasoline at a gas station in Florida 20 minutes after I bought my regular groceries in Arizona, so the bank flagged the transaction and called me. Another time it was used to buy household appliances in some distant state I'd never visited to be delivered to an address I had no connection with whatsoever.
Either way, dealing with the aftermath of the fraudulent credit card usage was only the most minor inconvenience. I don't understand why people get so worked up about such things: I'd be more concerned with my name, address, and other account details getting leaked since those can't be changed as easily (if at all).