Does the same grace that saves us also keep us?
Yes. The same grace of God that saves undeserving sinners also keeps them. Believers cannot live perfectly enough to maintain salvation by their own effort, so God continues to keep them by His grace. The applied blood gave them security, and grace provides ongoing security.
Les teaches that it is the grace of God that saves us, and nobody has trouble with that. He explains that we did not deserve salvation, but God saved us by grace. The problem is that many cannot comprehend that the same grace is what keeps us. Les says we do not deserve to be saved even six hours of the day, because we cannot live perfectly; we are human. So why does God continue to keep us? His grace, His grace, His grace. He illustrates this with the Passover: by faith they applied the blood, and God saw the blood and their faith, giving them safety. It was the blood applied that gave security and safety, and they could eat in calmness because God would keep His word. Likewise, salvation is never without blood, and the same grace that saves also keeps.