Before getting into details, it is important to note that the statute of limitations would prevent a claim beyond the past four years. There is also the question of damages -- if the grounds were properly maintained with less frequent visits, there is no damage from having a gardener visit less than once per month.
There's also an issue of waiver. If the landlord has been sending a gardener out only on occasion for sixteen years, a court may find that the parties' actual practices and the tenant's lack of complaint create a waiver of any responsibility for more frequent visits by a gardener.
There's also a possibility that the gardener is stopping by on a more regular basis, to check on the premises in between visits at which more work is performed, and hasn't been noticed by the tenant.
Absent actual proof of a breach and actual out-of-pocket damages to recover, suing seems likely to be a waste of time and money. Whatever the tenant decides in relation to the past, if the tenant is not happy with the gardener or gardening schedule, the tenant should direct complaints to the landlord and ask for the landlord to provide better service going forward.

