If you train in the morning, try to get up well before the class (1 hour) or avoid positions that bend the spine forward a lot. The spine is elongated after lying down when you were asleep which stretches and tensions it in a way that puts it at a higher risk of injury with extreme bending.
If you drive to class or sit on the side of class resting for a while, stand or walk around for a few minutes or do some cobra stretches. A prolonged bent forward spine temporarily changes the structure of the discs which we want to mitigate before doing activities where there are high forces on the spine, like the heavy lifting involved in a double leg takedown.
Try to rotate and twist through the hips, rather than the spine. The back can tolerate higher forces more easily in a neutral position. Using your spine instead may accomplish the technique you were trying to perform (a more powerful kick, escaping the back, passing the guard), but at the risk of injuring your back. In the same way, you may escape a guillotine choke but with a super bruised throat!