Gee, Dave, sounds like you don't know if you are coming or are going
If uke gives you their center in the attack, nage can just accept it and do a technique as long as uke keeps giving you their center - a lot of Aikido waza is taught that way. However, as you found out, if uke takes their center back (or does not give it up initially) nage must go and take uke's center and keep it for any technique to truly work. The former is a method where uke remains the attacker and nage remains the defender and the latter is where nage becomes the attacker.
IMO, nage needs to attack the attack and take
uke's center while keeping their own - in essence, they become the attacker and stay that way until they decide to stop the exchange - uke has no say in it while their center is not theirs. Sounds pretty simple and logical - but not all that easy; first, nage needs to learn how to control their own center before they can go off in search of other centers to control - I think someone once said that aiki starts at home, etc