Not all deadlines are created equal and if you have a lot of deadlines that feel random and meaningless with no consequence of missing them, then people will feel that and not take it seriously. Have deadlines that are relevant for the project, and explain the relevance of each deadline to the team, and you'll hopefully get better results.
> "I try to communicate with my team..."
This feels weird, when you ask them directly "Why did this milestone get missed, when it seemed on-track?", what are they telling you? Do they have other priorities and tasks from other managers? Else, what is going on? If you ask the other managers, what do they tell you? Are your team's priorities misaligned with your priorities? It feels like there are some basic conversations missing, or people aren't taking you seriously, or they have conflicting incentives.
> Perhaps there is some invisible work that gets in their way, or unexpected blockers waste too much time.
Invisible work and unexpected blockers aren't issues of motivation unless you are seeking to get them to work overtime to overcome these blockers.
> even if the milestones are aligned by everyone.
Everyone agreeing on something doesn't mean that everything is understood or correct.
It seems that your estimates are based on everything going right.
OP: Is their compensation and performance assessment linked to getting things done to your deadlines?
>> even if the milestones are aligned by everyone.
> Everyone agreeing on something doesn't mean that everything is understood or correct.
It could be the tyranny of the collective "we": "We should ship X by date Y". Is everybody clear on their individual deliverable to make that happen? When you do post-mortems after a deadline is missed, does everybody have a different picture of who was depending on who to deliver what? Was the root-cause of that lack of incentive, lack of buy-in, or your communication?