Betis dropped into the relegation zone this weekend following their 5-0 drubbing at Atletico Madrid and they have now lost four or their last five games in La Liga.
Things are going better in the Europa League, where Betis have taken five points from their opening three games to lie joint top of Group I with Lyon, but their domestic problems are a concern for the Seville-based club.
Nevertheless, Mel is determined to try and get his team out of their hole.
Asked at a press conference on Monday if he had thought about calling time on his three-year stint in charge of Betis, Mel said: "I had a hard time getting this job. I've worked very hard to be here, and the only thing I want to do is continue working.
"I cannot jump ship. I would be a coward, a bad professional.
"Now I have to work even harder. Keeping Betis up is more important than anything.
"We are in October and we still have time to turn things round."