It's not that your people didn't mean well when they volunteered for your project (or got the email that told them they were doing it). It's just that things change, and it's natural that people will prioritize in favor of the person or team that they're in contact with regularly and who holds the power over their performance reviews and paychecks.
Step 1: Make sure that you start your working relationship with a complete understanding of what the team is trying to accomplish and what everyone's expectations are- of their manager and each other. Among the things your team needs to state explicitly (so there's no wrong assumptions):
- The purpose and outcome of the team or project
- Expectations around communication frequency and method
- The percentage of their time or mind share they can commit to this project or team
- What else is going on in their workplace that might interfere
Step 3: Stay in contact with their boss. All too often that project that consumes us is an annoyance and drain on resources to others in the company. If the other managers haven't bought into the project it can create all kinds of problems. Among the things you need to discuss periodically are:
- The purpose of the project or team -- and why it's important to the company. Give them the big picture
- Expected time and resources
- How you'll handle conflicting priorities or challenges
- Update them regularly to keep them aware of the employee's good work and the status of the project
If you get the sense that people are being pulled in different directions, or your team members are choosing to spend their time elsewhere, you need to address it quickly and assertively. Find out what's going on and offer what assistance, resources or moral support you can.
Remind people about why the project matters, how it fits into the big picture and what's in it for them to stay focused on the work (bearing in mind that your job security is NOT their main concern). Run interference where you can and help them readjust their priorities.