It's worth the influence loss to prevent peerage. You'll get it back.
Remember, the AI characters aren't thinking about this. They aren't planning your downfall. It's just a math equation whether it comes up or not.
I've rarely seen it come up twice, let alone straight after. A third time would be quite the coincidence. So it's worth losing all your influence for, otherwise the next time you want to overrule them, you'll be looking at significantly more than that.
Perhaps, as a counter, you might want to propose and pass Royal Privilege: For Kingdom decisions, the influence cost of the ruler overriding the popular decision outcome is reduced by 20%. If you have a saved game... might want to go back to before they tried Peerage and get in first.