Probably wounded, i haven't played much sudden strike 1 but i remember this one. And the truck is the first aid truck.

I know this thread is from August, but it is still in the top of the list, so I would like to give a response to the question of why soldiers suddenly die, without being under fire:

In Sudden Strike 1 and 2 (never played the others) soldiers that have lost a certain amount of health can bleed to death, if they do not receive any help from a medic or ambulance truck. They do not die if they just lose a few of their hitpoints though, say if they have been hit and now have 80 instead of their 100 hitpoints, so they won't bleed out, because they still have enough hitpoints left to prevent bleeding, assuming that the wound is nothing serious. I am not exactly sure, how bad the soldier has to be wounded, before he starts losing hitpoints, approximately one hitpoint via a few seconds as far as I remember, but I guess from 50 points or lower he loses his remaining hitpoints, even when he is standing totally still. So, the only way to rescue him is by giving him medical attention, either with a medic or with an ambulance truck.

I remember that I have played a single mission (Huertgen Forest) and have carefully scouted the forest with an officer as well as a rifleman, to pick off enemy infantry one by one, as I normally do when playing Sudden Strike. Suddenly, my officer has been hit by a German rifleman. My rifleman killed the German soldier right after that, but my officer was losing his hitpoints. Because I have had no medic or ambulance truck, or they had been too far away to get to the officer in time, even if he would have walked to their direction while they are trying to get to him, I have ordered my rifleman to force fire on the officer, therefore giving him a coup de grace. That happened maybe 15 years ago or so, but I still remember that kind of dramaturgic war movie-like scene very much. Luckily, it was the only time I ever had to do that.

in the first mission your troops are already wounded and your first order is to take them into the ambulance trucks (red cross).
Second, you need to repair the 3 tanks in the north, right next to the troops across the street.
But be warned: a enemy bomber is trying to attack them, so you need to wait.

1. send your troops into the ambulance to heal them
2. wait for bomber attack to pass by.
3. repair 3 tanks

then, mission observer will give you your next orders.