At the beginning of the game you need to be careful about cross-pollinating. Until you are able to purchase better soil, most hybrids will lose health steadily until they die. The safest thing to do is to pollinate only similar or identical plants and sell them until you have enough money to improve your soil. You can usually find at least one common plant that will sell for upwards of $40, so it won't take too long to get better soil. As your soil improves, the number of more valuable hybrids that you can grow will increase.

Radioactive Plant Food will restore a plant to full health, but it's very expensive and most plants aren't worth that much at the beginning of the game.

Good luck, and please let us know if you need more help!