Gallium oxide (Ga2O3) is an emerging material for power electronics. The final penetration in the market is limited by several issues, including a stable and effective isolation between different devices and between different regions of the same device. In this work, we analyze lateral and vertical isolation structures, obtained by Mg implantation and annealing at 1000°C in Halide Vapor Phase Epitaxy β-Ga2O3. By means of repeated current-voltage characterization, it is possible to detect a severe current collapse, which can be completely recovered by white light illumination. When a constant bias is applied, the current collapse increases in magnitude at higher bias, showing a stronger filling of the deep levels. The transients closely follow the stretched-exponential model, an indication that the charge trapping is originated by extended defects, mini-bands or surface states. From the recovery transients carried out at various temperatures, it is possible to extrapolate a dominant thermal activation energy of 0.34 eV. The results of the recovery transients under monochromatic illumination show gradual variation in a broad energy range, consistent with the presence of extended defects. Temperature-dependent current-voltage characterization highlights the good performance of the bulk isolation and the presence of a significant surface leakage. Long-term stability tests show that the lateral structure is able to withstand a higher voltage level before catastrophic failure, but is less stable and is affected by a time-dependent degradation process. Charge trapping at the surface may act as a field-limiting element and partially explain the experimental findings.