Furthermore, every successful dictator has to project an image of excellent health.
After all, if your finance chief is loyal because you let him steal $10 million a year and he expects you to be in power for the next 10+ years, that's $100M+ for staying loyal.
If you're in poor health, though, and might only last 2 more years? Your finance chief is going to start thinking about who'll replace you. Earning that replacement's favour might be worth a lot more than the $20M he can expect from you.
Your military chief and police chief and religious chief are having similar thoughts, and before you know it your successor controls the treasury, armed forces and religion and you're forced into retirement or dead.
Granted, you can avoid the problem by having an obvious, powerful and deeply loyal successor. If Putin had a healthy young son he appointed the head of the armed forces he could be ill as much as he likes. But he doesn't have such a successor, so he's got to project an image of excellent health.