What does Satan do after failing to tempt Jesus the first time?

After failing the first temptation, Satan does not give up. He takes Jesus up into the Holy City, sets Him on the pinnacle of the temple, and tempts Him to cast Himself down, quoting Scripture that angels would bear Him up lest He dash His foot against a stone.

Les teaches that Satan doesn't give up after the first temptation. He takes Jesus up into the Holy City and sets Him on the pinnacle of the temple, with the temple crowds below able to see. Satan urges, "If thou be the Son of God, cast thyself down," citing the promise that angels would bear Him up. Les interprets this as the lust of the eye, a showmanship event like a Madison Avenue advertiser, imagining the impact on the crowd. Jesus refuses, saying, "Thou shalt not tempt the Lord thy God." Then comes the third temptation, the pride of life.

Matthew 4:5

Then the devil taketh him up into the holy city, and setteth him on a pinnacle of the temple,

Did Satan give up after failing to tempt Jesus the first time?

No. Scripture shows Satan did not give up after Jesus resisted the first temptation. He returned, took Jesus to the holy city and set Him on the pinnacle of the temple, urging Him to cast Himself down. After that refusal, Satan came with a third temptation, the pride of life.