What are the ways/strategies to maintain Drupal sites a over period of 10-15 years?
Like you mentioned there are many moving parts about Drupal that can require maintenance, so your strategy should be to remove as many dependencies as you can within your requirements.

If it is not a requirement that your Drupal sites continue as dynamic systems where content can be created, updated, or deleted then you should remove MySQL and PHP by generating static files. There is good documentation for creating static archives of a Drupal site at http://drupal.org/node/27882.

Since you mentioned putting the site into a "maintenance or dormant mode" it sounds like a static solution would be the best for you.

If you require the continual functional use of the site you could consider moving the site to a managed solution. Managed hosting providers can take care of the web and database server, but for further management of the Drupal code you could consider a service like http://drupalgardens.com.