Is a mistake made in the Istikhara when a girl refuses to be associated despite initial agreement and comfort after repeating the Istikhara prayer? And should he pray for their union or look for another girl?

If you seek Allah's guidance (istikhara) and ask Him to choose what is best for you, then do not grieve over what you have missed. For the acceptance or rejection of the girl holds good for you. You may earnestly desire something, yet it is evil for you, as Allah the Almighty says: "Fighting has been enjoined upon you while it is hateful to you. But perhaps you hate a thing and it is good for you; and perhaps you love a thing and it is bad for you. And Allah knows, while you know not." So, whoever performs istikhara should proceed with what they sought guidance for. Whatever comes to pass will be good for them. There is no harm in repeating the istikhara.