On August 3rd the CR definition of the Invest trait was changed so that the gold increase is now Permanent.
In reference to viewtopic.php?f=59&t=110632
If you negate the Recruit of a personality with an Invest trait the personality does not enter play, the gold is wasted and now their gold cost is PERMANETLY increased.
In rule question just posted, the Lion player's Ikoma Akinari would now permanently cost 17 gold as long as it is face-up.
Here is a follow up question.
I have Susumu Mizuki in my province.
I attempt to "Reserve" her into battle and decide to pay her invest. I pay 4 gold.
My opponent plays a Sun Returns negating an action. The gold is lost. Susumu Mizuki now permanently cost 4.
I try again to Reserve her and again decide to pay her invest. I now have to pay 5 gold.
My opponent plays a Interrupt the Void's Flow negating the action. The gold is lost again. Susume Mizuki now permanently cost 5.
My opponent plays Temple Grounds. Each time I try to bring her in, I lose the gold and her cost permanently increases by 1.