This has happened a lot of times in my career.
Why are employees leaving this company?
Lots of reasons; Moral is low, their friend was fired, they don't like the larger company, they are upset that the company they were with sold out, they are very very comfortable in their ways and can't handle the change and take it out the way they can, they are scared of being fired, don't see room to progress, followed someone else out the door.
Point is, it doesn't matter - as long as you enjoy the place you work don't get caught up in other people's reasons for not wanting to be at the company.
What does this signal for me personally?
Nothing unless you want it to, you are a contractor and the company still needs employees, especially ones that want to stick around after everyone else has left. This puts you on a good tier visibly in the new companies eyes.
What are the prospects for the company in the coming months / years?
This also can vary, you should research to see if the company that bought you out is an 'investment firm' cause if that's the case then they are going to milk the company dry in order to make a profit. This usual means that they will hire people at the lowest pay they can, give the current workers as little progress in pay as possible while also pushing everyone harder to make the company more valuable.
If you find the company that took over is actually interested in the current value of the company then you'll see the opposite. The company will put in a lot of care and tending to make it better and the employees within.
Either way you will see change, whether it's good or bad depends on you and the company that took over - you'll need to research the larger company to find more thorough answers for this.
Is there anything I can do to assist the company during this uncertain time period?
Simple answer, yes - be the change they want to see or work towards whatever it is that the larger company is focused on. Again, this is going to require you to research that company. You can also start meeting the new members of the higher ups (If there aren't any, there has to be someone that the larger company sends over) talk to them, ask them questions, bond with them.
How can I voice my concerns without coming across as aggressive?
You shouldn't and don't need to - you did just voice them on this forum. The company and management knows there are concerns, they are aware there is some discourse with all the change happening. Showing them that you are still there to do your job through it is the best thing you can do. Things change and that's normal, some people just can't cope with it - being someone who can will show them how valuable you are.
What is the most productive approach to discussing this sensitive issue with my manager?