The high dose conformity and healthy tissue sparing achievable in Particle Therapy when using C ions calls for safety factors in treatment planning, to prevent the tumor under-dosage related to the possible occurrence of inter-fractional morphological changes during a treatment. This limitation could be overcome by a range monitor, still missing in clinical routine, capable of providing on-line feedback. The Dose Profiler (DP) is a detector developed within the INnovative Solution for In-beam Dosimetry in hadronthErapy (INSIDE) collaboration for the monitoring of carbon ion treatments at the CNAO facility (Centro Nazionale di Adroterapia Oncologica) exploiting the detection of charged secondary fragments that escape from the patient. The DP capability to detect inter-fractional changes is demonstrated by comparing the obtained fragment emission maps in different fractions of the treatments enrolled in the first ever clinical trial of such a monitoring system, performed at CNAO. The case of a CNAO patient that underwent a significant morphological change is presented in detail, focusing on the implications that can be drawn for the achievable inter-fractional monitoring DP sensitivity in real clinical conditions. The results have been cross-checked against a simulation study.