Can you make RRSP contributions after the age of 71?

Your RRSP contribution is limited to 71
Bob, I can understand your confusion because you and your wife have converted your RRSP into a registered retirement income fund (RRIFS). RRSP account holders need to do this before December 31, at least 71 years of age or older.
There is a location in your NOA and CRA online account that can report your RRSP room, so the CRA will provide your RRSP deduction limit even if you no longer contribute to RRSP. If you are over 71 years old, you can’t usually do anything with the RRSP room. That is, there may be an exception.
Contribute to spouse RRSP
If your spouse is 71 years old or under, he or she can open the spouse RRSP. A spouse RRSP is an account owned by one spouse (usually a lower income or younger spouse) and contributed by another spouse to another spouse who is usually older or higher income.
As long as you contribute to the spouse RRSP of your younger spouse, you can make RRSP contributions at age 71 or older. When doing this, you use your own RRSP room and deduct the deduction based on your own tax return. The spouse RRSP account holder will withdraw money in the future.
Can you have both RRSP and RRIF?
Even if you have converted RRSP to RRIF, you can still make RRSP contributions. This is because you can have unlimited RRSP and RRIF, and when you convert RRSP to RRIF, you only do this for that particular account. You do not have to convert all accounts at the same time.
If you are over 71, you can even transfer RRIF funds back to RRSP and stop RRIF withdrawals. Although this is not common, it is technically rare.
The only time you might want to contribute to RRSP after converting RRSP to RRIFS is if your income or cash contribution surges and you want to ask for an RRSP deduction.
Unused RRSP contributions
Interestingly, you can contribute to RRSP until you get over 71 years old and make a deduction. These unused RRSP contributions can be deducted in the future without age limit.