Rare

Draws in Jerome Gambit (1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Bxf7+) thematic tournaments are quite scarce, showing up about 3% to 4% of the time, on average, according to my database.

So it is only fair to mention the recently completed game eddie 43 - Black Puma, from the ongoing Jerome Gambit Thematic Tournament at Chessworld, which reached the following position after White's 45rd move.

Black has played solidly, and has even increased his piece advantage to a Rook advantage; but here he sees the chance to create a passed pawn and intensify pressure on the enemy King, so he grabs an expensive pawn...

45...Bxd3 46.Qf5+ Kh8 47.Qf8+ Kh7 48.Qf5+ Kh8 49.Qf8+ Kh7 50.Qf5+ Kh8 51.Qf8+ Kh7 52.Qf5+ Kh8 53.Qf8+ Kh7 drawn