Amalykites were a problem for Israel while they were in the wilderness. Turns out they were were also in the promise land along with a whole bunch of new giants and enemies.
Just when you are about to get a taste of the promise, all the enemies old and new are standing between you and the promised land.
The 12 spies returned from the promised land, 10 of 12 saw only the natural, and had a natural reaction to it. They said “we were in our own sight as grasshoppers”. All 12 saw the same things, but had different reactions to it. The spies only considered their natural capabilities (instead of trusting God’s capabilities). The 10 spies are in effect saying God is foolish for giving them the opportunity to enter the promised land.
Saul did not kill off the Amalykites once and for all when he had the chance, so they continued being a problem.