Automated extraction of individual plant branches from time-series imagery is essential for high-throughput phenotyping, yet it remains computationally challenging due to non-rigid growth dynamics and severe identity fragmentation within entangled canopies. To overcome these stage-dependent ambiguities, we propose ST-DETrack, a spatiotemporal-fusion dual-decoder network designed to preserve branch identity from budding to flowering. Our architecture integrates a spatial decoder, which leverages geometric priors such as position and angle for early-stage tracking, with a temporal decoder that exploits motion consistency to resolve late-stage occlusions. Crucially, an adaptive gating mechanism dynamically shifts reliance between these spatial and temporal cues, while a biological constraint based on negative gravitropism mitigates vertical growth ambiguities. Validated on a Brassica napus dataset, ST-DETrack achieves a Branch Matching Accuracy (BMA) of 93.6%, significantly outperforming spatial and temporal baselines by 28.9 and 3.3 percentage points, respectively. These results demonstrate the method's robustness in maintaining long-term identity consistency amidst complex, dynamic plant architectures.