A much fuller description of the site would make any answer also fuller and more useful. If the situation lends itself to this, then a good geotextile should be capable of solving the problem for years to come. It would in essence go in place of the tarpaulin. People like B&Q sell geotextile (perhaps referred to as something else, but found in the gardening section) by the metre. Buy the strongest and lay it double or even triple. Since you say the garden sank, presumably there was soil and vegetation over the tarpaulin for years - it should not be difficult to re-establish it.