Every escape artist has a signature route
Dogs rarely escape at random. One dog is a squeezer who flattens under the gate where the ground has dipped. Another is a climber who uses the compost bin, then the fence rail, then the top. A third waits for the side gate latch to bounce and shoulders it open. Walk the boundary at your dog's eye level, looking for daylight under panels, loose boards, gaps where the fence meets the house and anything stored against the fence that works as stairs. If you cannot find it, watch a garden session from a window, or ask a neighbour which side he appears from. Fixing the route he actually uses matters more than raising the whole fence for a dog who leaves at ground level.
Repair the boundary in the order he exploits it
Close the ground gaps first: a solid threshold under the gate, boards reset and screwed rather than propped, and dips along the fence line filled and firmed. Move bins, benches and log piles well away from the fence so the climbing route loses its first step, and check that latches close with a positive click and cannot be lifted by a nose or a jumping paw. For a determined digger at one panel, the fix is at the base of that panel, buried mesh or slabs, not along the whole run. After each repair, test honestly by letting him into the garden while you watch, because an untested fix is only a hope with screws in it.
Make staying in the garden more interesting than leaving it
Many escapes start as curiosity about a more exciting world: dogs passing, children playing, the sounds of the street. A dog whose garden time is mostly alone time has every reason to go and find the action. Give the garden its own events, a sniffing game scattered in the grass, a game of fetch, training practice with real rewards, and your company for part of the session. Keep him on a long line attached to a harness during this retraining period whenever you cannot watch closely, so freedom returns gradually rather than all at once. A dog who has had a proper walk before garden time patrols the boundary far less than one let out full of unused energy.
Plan for the day a repair fails anyway
Even a well-kept boundary meets its match eventually, a storm-damaged panel or a gate left ajar by a visitor, so layer your safety. Make sure his collar fits and carries your current contact details, that he comes when called at the gate even when excited, and that the whole household knows to check the latch out loud during busy comings and goings. If he injures himself on a fence during an attempt, cuts a pad or catches a leg, get veterinary advice the same day rather than waiting to see how he walks on it. Should a gate be left ajar anyway, his KinsLe profile already carries the Lost Pet Alert System at no cost; finders checking the map can reach you by direct message.