Just because your manager dos not mean your not human. Managers also get sick.
Suffice to say we all have extra responsibility as managers and are required to get the job done, while we are away. Is that not why we have staff, to get the job done. Delegation of responsibilities so to speak.
Even if it is for one day, a week etc.
I would be more inclined to explore reasons why your work, is not done on the day you happen to call off sick. Yes, it is a rare occasion, but ultimately your staff (even second in charge) should be able to perform your duty when you cannot come in.
This sounds more like a lack of training in lower level staff, who work under you which is the problem.
At least that way, when you do call in sick on the rare occasion. You tell your boss, " Jenny can take care of things today, she knows what to do, i have already spoken withher"
Then your boss, knows the work will get done, you have organised it and put well traind personel to take your work responsibilities for the day.
As opposed to dumping the responsibility onto the boss, to organise all that for you.
Whenever i call in sick, as a manager. I make sure i speak to my staff first and inform them of the important things that must be done that day.
Then a second phone call to the boss, informing them that im sick, and that my staff are aware and looking after the work that needs to be done.
The company is always bigger than one man. In fact its a team. So whoever i have working for me, i make sure that they can do everyone elses job, they are versatile and flexibile in their work responsibilities. Rotating their work so they can do other peoples jobs is an essential part of the business.