If another faction refuses the large gift, then the small gift, while still in the same window you can keep clicking until they randomly accept the gift--at least in this case they did. Should probably lock out offering a gift for a few turns. But very minor--a simple work around is to just not keep clicking on offer gift. And maybe even leave it as is for players desperate enough to keep clicking it until they accept. I was just kind of absent mindedly clicking while thinking about something else and was surprised on the 5th click they accepted it.
Yes, it didn't make sense for a faction to refuse a large gift but then consider accepting a smaller one in the context of the same discussion. A fix went up to address that today in the 1.3.0 update. Thanks for mentioning this. As for additional clicks, when a faction makes up its mind with respect to a gift and decides to not accept it, it should not make any difference how many times you try as they will keep saying no, at least in that discussion and from what I remember when I last checked the code.
In this case they had rejected both the small and large gifts and I just kept clicking between them and suddenly they accepted one. I'm not using the beta though so might already be fixed in 1.3.