In the current industrial landscape, increasingly pervaded by technological innovations, the adoption of optimized strategies for asset management is becoming a critical key success factor. Among the various strategies available, the “Prognostics and Health Management” strategy is able to support maintenance management decisions more accurately, through continuous monitoring of equipment health and “Remaining Useful Life” forecasting. In the present study, Convolutional Neural Network-based Deep Neural Network techniques are investigated for the Remaining Useful Life prediction of a punch tool, whose degradation is caused by working surface deformations during the machining process. Surface deformation is determined using a 3D scanning sensor capable of returning point clouds with micrometric accuracy during the operation of the punching machine, avoiding both downtime and human intervention. The 3D point clouds thus obtained are transformed into bidimensional image-type maps, i.e., maps of depths and normal vectors, to fully exploit the potential of convolutional neural networks for extracting features. Such maps are then processed by comparing 15 genetically optimized architectures with the transfer learning of 19 pre-trained models, using a classic machine learning approach, i.e., Support Vector Regression, as a benchmark. The achieved results clearly show that, in this specific case, optimized architectures provide performance far superior (MAPE=0.058) to that of transfer learning which, instead, remains at a lower or slightly higher level (MAPE=0.416) than Support Vector Regression (MAPE=0.857).