They've simply changed their minds about the situation.
Just before his death, Robert tells Ned he was right, and ask him to cancel the assassination.
"The girl," the king said. "Daenerys. Let her live. If you can, if it... not too late... talk to them... Varys, Littlefinger... don't let them kill her."
(A Game of Thrones, Eddard XIII, Bantam Books Mass Market International Edition, page 505)
This may even have happened before the assassination attempt on Daenerys in Vaes Dothrak, but unfortunately they couldn't cancel it because the order had already been sent.
"Robert had a change of heart concerning Daenerys Targaryen. Whatever arrangements you made, I want them unmade. At once.
"Alas," said Varys. At once may be too late. I fear those birds have flown. But I shall do what I can, my lord."
(A Game of Thrones, Eddard XIII, Bantam Books Mass Market International Edition, page 508)
Shortly after, the War of the Five Kings started, and Daenerys was more or less forgotten for a while. Moreover, after the death of Viserys, Drogo and Rhaego, Daenerys was left with barely a hundred Dothrakis (mostly old men, children and women) instead of 10 000 warriors, and they went in the desert east of the Dothraki Sea. The problem seemed to have sort itself. The Small Council only took interest in her again when they learned that she had conquered Slaver's Bay and that she had live dragons. At that point she was a potential danger again, so they sent a new pardon to Jorah to make Daenerys doubt his loyalty and send him away.
Additionally, Joffrey had no personal reason to hate the Targaryens like his
father predecessor, which can explain the lack of interest for Daenerys.