I read this post again and I'm a male telling you he is not maintaining his erections with you because this other woman's vagina makes his penis feel so much better.
The only way you can get him back is having him leave that woman alone completely. Eventually, his penis will get back use to the way your vagina pleases him and the marriage will be fine.
But the hardest part is getting him to leave that woman alone. You opened a big can of worms.
Yes, Rules are rules. But rules are always broken sometimes, right? Human nature is above all that. And a person cant stop his/her emotions. I would just never advise this, there are so many other crazy sexy ways and things to do, but you know for sure how it will turn out. it the long run, They may develop feelings towards eachother. If hes still getting up for the other woman, and can not get up/ or stay up for you then there is Really a problem. Either he is not attracted or it doesnt feel the same. Or He is not in love anymore but trying to do the right thing and be with you. Or most likely something is more sexually attracting over with the other woman ie. he may have better sex, he may be falling in New love with her, He may really wish to be with her or enjoy his time, she may be pulling in that direction also; But he still 'Loves' you (as in "i love her because shes my wife) so when he tries to be with you he wants to but it just doesnt work, maybe feels bad, maybe sexual desire drops.
Only way you will know is if you ask! You need to confront him. and tell him how you feel. Dont accuse (yet, atleast) but explain to him that at this point in your marriage you need him and him only, and you need him all to yourself. Tell him that the swing must stop. Make it about you guys, about a happy thing, through in a vacation or something so he doesnt get defensive. You will know how he feels if/ how much he argues about seeing her. And if he actually does!
Bottom line... Youre his wife and he is youre husband. this should be stopped.
To me it sounds like this other woman pleases him better in the bedroom. Her vagina may feel way better than yours (more tighter, more grip, more sensation). Sorry to break the bad news to you!
This is why husbands and wives shouldn't have sex out of their marriage. Sooner or later you're going to experience some better sex than what you have at home.