I'm faster at 51, than I was at 21, or 31. As you get older, you've got sevral things working against you. One, it takes longer to recover from hard days; Two, you're more likely to have chronic illnesses (such as the OP's arthritis) and Three, your absolute potential drops overtime, most notably for explosive power, i.e. sprinting.

All of those things explain why you don't see people winning the Tour de France, past age 35, or Classics past age 40.

However the vast majority of us never approach our potential limits. Thus at 61 you can still be fast, perhaps faster than you were at 41 by realizing a greater percentage of the potential you still have.

To do that you have to train, eat, and rest, better and smarter. If it's enough of a priority, and assuming your arthritis and asthma are not diasbling, I guarantee you that you can still be fast enough to dust most any recreational cyclist regardless of age, and be competitive in Masters races.

In onther words your age, and the problems associated with it are obstacles, it is not an absolute limiter.