The company for which I work has been bought and sold a few times, and each time, the policies change somewhat. Early on, there was no sick leave. Then there was sick leave, but only for when the employee was sick. Then the sick leave became viable for things such as sick dependents, then it morphed into PTO, then back to sick leave, etc.
Over the course of the years, there has always been a cap on how much sick leave/PTO/Vacation/etc. time could be accumulated. For the most part, sick leave was not allowed to be carried over. I have worked with a great number of great people, and many of them are much like the OP - worked for 20 plus years and never used sick leave. Early in my career, I used sick leave if I was sick, then if the kids were sick, etc. When we started using PTO, it didn't matter what you were doing - sick or well - you just didn't have to come to work. Currently, we are back to having separate "Occassional Leave Days" and vacation time, with limited carryover of each.
I use all of my time every year.
Why? I became jaded to the corporate mandates very, very early. At my location, at least, we have yet to give out the very first award for "Working While Sick". Personally, I rarely get sick. It doesn't bother me if someone else comes to work sick, but I'm not admiring their dedication either.
"Back in the Day" of family-owned businesses, personal sacrifice probably was noticed and potentially rewarded. In the business world today, with interchangeable management components, there's a good chance that my boss today won't be there in a couple of years and he wouldn't remember how many days I missed and how many I didn't.
I'm already of the assumption that I'm probably going to have to be gainfully employed in some capacity until I'm at least 70 - at least that's what I tell myself. We already own our property and home free and clear (except for taxes, of course), are generally healthy and live well but not lavishly. However, I tend to be a bit of a negaholic about things, and beyond my wife, I don't trust anyone about anything (especially coworkers!). I have also witnessed many people work tirelessly year in/year out, chained to their jobs (which is what I feel I am interpreting from the OP), planning to enjoy their retirement, only to have the rug pulled out from under them due to changes in their employer or their health.
I try to live every day as a good day, and not put off rewarding myself until retirement. If I can sneak out 15 minutes early (I'm salaried, so I'm not on the clock anyway), then I do. I'm an early riser, and generally spend 9-10 hours per day at work. Due to the nature of my job, sometimes I work weekends and holidays to complete projects while the manufacturing plant is down. However, if I do that, I take off some "comp time" - informally - to make up for it.
This may be coming across as though I am a slacker, but I don't feel that I am. I give my time and talents to the company in exchange for payment, and that is likely where my dedication to them, and theirs to me, ends. I don't shirk my responsibilities, but I know that giving more of myself will not result in any better rewards.
In the end, the decision rests, as others have said, with whatever you can personally deal with, morally and ethically. If you feel that taking the time off is immoral and unjustified, then ride it out to the end with that, and sleep well at night. Or, start taking time off and tell yourself that you are overdue for it.
I work in a facility that (more or less) operates 24/7/365. We have had many folks that are like the OP - integral to the operation, on call when they are not here, etc. Irreplaceable, or so they think. I've seen dozens of "irreplaceable" people come and go, sometimes of their own accord, sometimes otherwise. Does it cause a temporary hardship? Of course. But the business moves on. I feel that being so dedicated to a company, and being so important to it, can be a bit of a martyr complex, but that is up to the individual how much they will allow for a company to intrude upon their personal life.
Some of my favorite memories with my children and wife have been when I've taken the day off to use up accumulated time for the year. Those that let their time go to waste got neither compensation nor prizes.
Over the years, I've mowed a lot of cemeteries. I have yet to trim around a tombstone that reads "I Wish I Spent More Time At Work."
Sorry about the dissertation. Didn't really think that I had that much to say, but it is a current topic at my workplace, due to a recent change in ownership, so this subject is very much at hand in my personal life. In the end, make whatever decision suits you best, and I wish you well.
Good luck and take care.