Eve online to many is under going a phase of stagnation. It's been a long phase, with many suggestions on why it exists and what can shake things up a bit.
Here's my suggestion expanded from a back and forth twitter session earlier this evening.
Sovereignty based on activity. In order to claim a system it has to be used and that usage has to be maintained. Based on the number of hours/week/system with different activities given different weightings.
Much like the industrial and combat index level that opens up more and more content, a sovereignty system based on character activity is I believe the most logical method of awarding alliances the existing bonus's for their effort, co-operation and space holding desire.
The activities shouldn't be limited to one factor but the whole aspect of activities within Eve, mining, manufacturing, pve content and of course PvP activity level. Add in gate jumping to the index level and even poor true sec level pipe systems can slowly be maintained.
This does mean of course that systems will need to support more players than I feel they're currently capable of. With the coming industrial changes in the Crius update, at least this has been achieved in a pretty large way.
TL:DR Want sov in a system - use the System. I know balancing may be an issue - too high and offensive policies may be difficult, too low and flipping system sov too easy. If it means players have to undock and participate in the Eve, it can only be better than un-docking and jump bridging in order to shoot structures for 3+ hours.