Mecklenburgh was shown discovering her co-star's flirtatious posts and requests for nude pictures in the latest episode of the ITV2 reality series on Wednesday (February 1).
The show closed with the glamour model refusing to see Falcone, prompting him to take to Twitter and beg for forgiveness.
"Everyone makes mistakes.. I am only human," he wrote. "I am so sorry for hurting you @lucy_meck... I will always love you baby x."
The couple briefly separated last year after Mecklenburgh lied about cheating with ex-boyfriend and former TOWIE star Mark Wright.
Falcone said later that they were having issues "trying to establish trust" in the wake of the affair.
"It's not about forgetting - it's something we both have to learn from," he said. "It will always be at the back of my mind."
The Only Way Is Essex airs Sunday (February 5) at 10pm on ITV2.