Is it possible to make a subscription of a product (like a rental product)?
It is. The important bit is how you do the billing in this case. There are several good options for recurring billing e.g. stripe with its https://stripe.com/subscriptions is one of them.
I need something like this too, has there been any progress made here?
Boomer Digital has started a Reaction plug-in for subscription recurring billing: https://github.com/boomerdigital/reaction-subscription-billing/
More details on their approach and the features: https://github.com/boomerdigital/reaction-subscription-billing/wiki