There are several soft techniques for trying to beef up participation that I am sure others will elaborate upon. I am going to restrict my answer to how you should handle it if you are unable to get traction with your participating resources:
Resources that need to participate in a project to make it work are almost like external resources (e.g. raw materials), if not enough of them are provided, then the project cannot deliver to its objectives.
This situation should be managed in the same way as external resources running out or not being available, i.e. through your active risks and issues management.
If you know this is a problem in your organisation then raise it as a risk in your risk log right at the start, and ensure you are sharing and reviewing your risks with your Project Board/Steering Group/Sponsor/Manager/Whatever.
Plan your project knowing about the scarcity of these resources and include contingency time for delays caused by lack of participation and cite the risks you have raised as the cause of the contingency planning.
As participation dwindles, increase the profile and likelihood of the associated risks and continue to actively manage and review those risks with the appropriate authorities. Seek assistance from your authority to help mitigate the risks by (with any luck) applying pressure from above- use your Project Board to help you solve the problem.
If participation dries up, close the risk (or change it) and definitely raise a big fat issue on your issue log. Immediately notify your Project Board (or other authority) of the issue and its effects, i.e. to go into contingency mode and commence re-planning based on lack of the resource- If you no longer have the raw material your delivery date must start to move to the right.
Do all this publically (whilst obviously observing political sensitivities), openly, factually and without emotion playing a part. All that happened is that a resource over which you have no control failed to materialise, you are not responsible for that, you are only responsible for reporting its effects and trying to mitigate it with other project actions, such as seeking alternatives and re-planning delivery dates.
Risk management is your friend. Use it. All the time.