Software aging refers to the performance degradation and failure crash phenomena in long-running systems. As a proactive remedy, software rejuvenation can be scheduled timely to mitigate aging effects. Inescapably, how to accurately predict the time to aging failure (TTAF) of software is a prerequisite for implementing effective rejuvenation. However, the characterization of software aging is relatively complicated, leading to the selection of aging indicators case by case, which means that only fitting the variation trend of a single indicator for prediction models to formulate a rejuvenation schedule may be limited. To fill this gap, this paper proposes a novel framework called TTAFPred, which directly constructs the direct mapping relationships between the software aging process considering multiple system indicators and TTAF. Specifically, this framework includes three parts, i.e., data preprocessing, software degradation feature extraction, and TTAF prediction modules. First, the raw data is processed into the input form required by the network. Secondly, a temporal relationship extraction stream integrating bidirectional gated recurrent unit (BiGRU) with attention mechanism is used to extract temporal features from raw inputs. Synchronously, a spatial relationships extraction stream is adopted to extract the spatial features for enhancing the representation ability of degraded features by using the multiscale one-dimensional convolutional neural network (1DCNN) with the residual connection. Then, extracted temporal-spatial features from the two streams are further fused. Finally, two fully-connected layers are constructed to estimate the TTAF. The experiments are performed on two mainstream software systems (OpenStack and Android), and four sets of real run-to-failure data for each software system are collected. The effectiveness of the proposed TTAFPred is verified through extensive experiments with its seven competing models, and the prediction performance can be improved by 9.1%, 8.0%, and 8.0%, respectively, in terms of three evaluation metrics, compared to the best baseline model.