We are witnessing an emergence of a new era of applications delivered via a paradigm of flexible and softwarized communication networks. This has opened the market to a wider movement towards virtualized applications and services in key verticals such as automated vehicles, smart grid, virtual reality (VR), Internet of Things (IoT), industry 4.0, telecommunications, etc. With an increasing emergence of verticals driven by the vision of low latency and high reliability, there is a wide gap to efficiently bridge the Quality of Service (QoS) constraints for the end-user experience. Most latency-critical services are over-provisioned on all fronts to offer reliability, which is inefficient in the long run. In this work, we present a Residual Long Short-Term Memory (LSTM) based multi-label classification framework for proactive SLA management in a latency-critical Network Function Virtualization (NFV) application use case. We compose a multivariate time-series forecasting model with multiple time-step predictions in a multi-output scenario, and associate a multi-label classifier for a granular prediction of individual Service Level Objective (SLO) violations for each step in the forecast horizon. The Residual LSTM approach achieves an improvement of 31.1% over the baseline on the forecast classification accuracy, and a 2.65% improvement on the interpolated average precision over the standard LSTM methodology.