I try and stay out in the rain as much as I can. If Im in a box blind I will stick in out and try to stay alert. I will admit, I do see fewer deer when it gets beyond a drizzle. If it gets heavy and I put my head back and take a little nap, waking up every 15 minutes to take a look. I probably have missed many deer that way, but I don't think too many. I did fall asleep once in a ground box blind and wake up and have 3 does 15 feet away and I wanted to fill my doe tag that day too!
If im in my climber or ladder stand, I have rain gear to wear but if it gets bad, heavy down pour or lightning, Im heading in. I watch the weather though carefully. If it has been raining all day and plans on letting up before dark, I want to be in my stand when the rain stops. If the deer have been laying all day, there going to want to get up and move around as soon as its over.