Lost from follow-up, after starting moderate acute malnutrition (MAM) is an ongoing challenge of public health until the admitted children reached the standard weight of a reference child. Thus, the present study aimed to assess the rate and estimated time to attrition after under-five children started treatment for MAM in the Gubalafto district. A facility-based retrospective cohort study was employed among 487 participant children who had been managed targeted therapeutic feeding from 1 June 2018 to 1 May 2021. The overall mean (±sd) age of the participants’ children was 22⋅1 (±12⋅6) months. At the end of the study period, 55 (11⋅46 %) under-five children developed attrition from the treatment after starting ready use of therapeutic feeding. After checking all assumptions, a multivariable Cox regression model was used to claim independent predictors for time to attritions. The median time of attrition after starting treatment of MAM was 13 (IQR ±9) weeks, with the overall incidence of attrition rate reported at 6⋅75 children Per Week (95 % CI 5⋅56, 9⋅6). In the final model of multivariable Cox regression, the hazard of attrition was significantly higher for children from rural residence (AHR 1⋅61; 95 % CI 1⋅18, 2⋅18; P = 0⋅001), and caregivers with their dyads did not get nutritional counselling at baseline (AHR 2⋅78; 95 % CI 1⋅34, 5⋅78; P = 0⋅001). The findings of the present study showed that nearly one in every eleven under-five children was attrition (lost to follow-up) in a median time of 13 (IQR ±9) weeks. We strongly recommended for caregivers provisions of diversification of daily nutrition supplementation of their dyads.