This is diffcult to diagnose without seeing the full VPN configuration of both the CheckPoint and Fortigate.
Checkpoint uses DPD and I believe Fortigate uses Auto Keep Alive so, even if these are configured and working, dropping the tunnel due to inactivity may not be the problem.
Before you go to deep into troubleshooting, however, one thing I would ask you to check is the LifeTimes on the CheckPoint side for Phase I and Phase II match the Fortigate side and that on the Fortigate side, the Phase II KeyLife is set to Seconds and not "KiloBytes" or "Both" . If the Fortigate is using KiloBytes as the key life time, it could try to create new keys before the CheckPoint is ready. This makes the re-key unpredictable as it's dependent on how much data has been processed in any given time period.
If one side tries to regenerate keys before the other side is ready you will have problems with the tunnel.