Is there a regulation that requires manufacturers to cover AD's for the life of the equipment?
The answer is basically no for aircraft not under warranty, but...  

I've participated in numerous AD related activities on the OEM side, and I've never seen an AD with a commercial policy incorporated into it that dictated who pays for compliance, kits, or labor. 

So strictly speaking, the aircraft operator is on the hook once an aircraft is out of warranty, but the OEM will normally have an internal commercial policy in place that its program office, customer support organization and spares organization uses as guidance on charges.  

There is usually a Service Bulletin with a kit that has to be incorporated to terminate an AD and the OEM will decide whether to make the SB and kit available free of charge for some period of time when it's required to comply with an AD, for reasons of morality, politics and marketing. The commercial terms will be included in the Service Bulletin. 

That is probably typical, but if an OEM is in a financially tight position and an AD's compliance is really expensive, the OEM may decide to make the operators pay for the SB and kit, or the costs related to a repetitive inspection, and take the heat by getting yelled at during operator conferences. 

And sometimes, as in your case, if labor is significant, the OEM may also include a labor charge-back policy that will refund labor costs based on the estimated man-hours quoted in the Service Bulletin. 

Sometimes operators include out-of-warranty "AD clauses" in their purchase contracts to avoid getting burned. And sometimes operators, especially those that may be looking for more aircraft, cut their own deals on the side.

Another factor is that, in order to get less onerous compliance terms or limitations in the AD itself (as I suspect in your case), the OEM may convince the regulator that they plan to proactively "campaign" a mod free of charge including labor charge backs, with a campaign completion date, and which may even include sending out dedicated teams to do the work (as with the Cardinal stabilator slot mod).  Sometimes this is enough to avoid an AD being issued at all if the regulator is satisfied that every affected aircraft will be fixed by a certain date.