A Biden administration official says that Ukraine can keep the offensive going for around six to seven weeks more, and there are private disagreements over how much progress can be made in that time.
Given that AFU having abandoned most of their reserves to break through the defence line and suffered heavy losses while trying to break through it, are unlikely to be able to go far.
Meanwhile, according to a senior US intelligence official the quality of Ukrainian forces is declining over time.
Finally, US officials have criticized the Ukrainian military strategy, in particular for the decision to deploy experienced units in the east, near Bakhmut, rather than in a key area in the south.
It looks like AFU is now stretched thin across the line of contact and isn't able to concentrate sufficient numbers of troops in any one area to make significant progress. Russian offensive in the north means that Ukraine can't pull troops to the south without sacrificing their positions. However, the west wants to see visible progress and pressuring them to do so.
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There it is, then. I didn't realise the connection between the retreat and the referenda.
Although I at least knew there were referenda, even now I talk to people who have no idea that those regions held a vote at all. The propaganda worked.