There's an interesting dicusssion on RSR about how to prevent your back opening up too early w hen training on a rowing machine.  Here is a great answer from A3aan

On a static erg there is slack at the catch; after sliding forward the handle moves a significant distance before you feel resistance. This encourages opening the back too soon. To avoid this, try using a Concept II with slides, or even better a RowPerfect erg.  On a static erg I try to solve this by reaching out as much as possible with hands an shoulders and not kicking too hard at the catch.

Furthermore I believe maintaining good back posture during the first phase of the stroke is not only technically hard, but very hard work as well. To be able to do it, and keep doing it right for a longer piece of rowing, you need strength and endurance in your corset musculature. Therefore I train my high/low/side abdominal muscles and back muscles after each erg workout. Also I throw in some stability exercises like pushups and sidehangs (hard to describe).

Caroline Tu replies with a nice practical exercise

one thing you could think about is that perhaps you are lifting your shoulders at the catch.  This in turn could be caused by dropping your hands as you come forward.  You probably don't do it in the boat, as you would see your blades "skying".

An exercise you could try is to work up the slide from frontstops – quarter slide, half slide, three quarter slide, full slide, using legs only and concentrating on keeping the hands level. Aim at a suitable point on the ergo – e.g. the top of the slot that the chain comes  through.   If you can do it with a mirror, so much the better.