I am not a lawyer; this is not legal advice.
But if they don't [list for rent and sale] this suggests that expenses which were previously deductible are no longer.
That seems reasonable. A few paragraphs earlier, that same page has (my emphasis):
You can deduct your ordinary and necessary expenses for managing, conserving, or maintaining rental property from the time you make it available for rent.
So, if being able to deduct expenses is only possible from the time it is available for rent, it would be logical that if you stop making the property available for rent, then you stop being able to deduct expenses.
I can't imagine people often list units for rent and sale at the same time.
I have never been a landlord, but I see little reason why you shouldn't continue to list the property as available for rent while trying to sell it (assuming you're selling it as a rental property, with the expectation that the buyer will continue to rent it out):
You don't know how long it will take to sell: refusing to rent it during this process could be a significant loss of (potential) rental income, especially if expenses are not deductible when not on the (rental) market.
If one or more tenants approach you when you are close to completing a sale, their interest may make the difference if the buyer is wavering: the buyer will have (potential) tenants without having to advertise.
Even if some tenants may be put off by the fact that your are in the process of trying to sell the property, you will be no worse off than if it wasn't on the rental market (and – if expenses aren't deductible when off the market – you will be better off because you've at least tried to rent it, and so can deduct expenses).