As taught in BBT, the press (2.0) begins with the hip drive. I find that when doing multiple rep sets (i.e., 3 or 5 reps), it is much easier to initiate the first rep with the hip drive, and immediately press the second rep without completely re-setting (i.e., exhaling and taking an entirely new deep breath). I don't seem to lose tightness by doing that. Before rep #3, I exhale, take a new big breath, and begin the rep with the hip drive.
Is it preferable to completely re-set before each rep, or is this a method that others use as well?
Both are good methods, but the hip-movement on every rep is going to incorporate more muscle mass and allow you to make longer and more progress. You're probably fine, but I would encourage you to switch to a consistent hip-movement press at some point. The fact that you lose tightness by exhaling and taking a new breath is not an inherent problem in the technique. It's something you need to control.
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