Not sure how accurate this is as I haven't taken notice, but I was told by my leader that all the extra summon fragments from our summon fights are converted into chakra points to upgrade the summon. 1:1 ratio.

I don't see any reason to not put all chakra into the summon, but there is always that chance that a new one will be released. But as we don't know how long that will take, I would put all you can into the current summon.