Like many have stated, it depends largely in the gymnast. But equally important is what level as well. I'd say levels lower than 7, you can probably go two weeks. Levels 9 and 10 one week. This is probably the most I woukd go mid season. Summer, I may go longer.
My daughter took a month off at old Level 4 right at the start of meet season, competed I think a week later and won the meet. She didn't do a trace of workout. Level 5 we took three weeks off straight and she was training for TOPs. In a week, she was back on track. Level 6, 7 and 8 if I recall correctly (I remember the earlier years more because being new to gymnastics, I too were concerned), we took two weeks back to back and a week some other time. She was again training for TOPs. Our family/relatives are in the other side of the country. So we always make a trip out there every year. Level 9 we took two weeks. She was back on track after a week. She was injured end of Level 9 and out of gym for 6 weeks. Lost some skills and took about 2 months to be back on track. This year, Level 10, she was injured after first meet and was out for six weeks. It took almost three months to where she had alk her skills back and competition ready. We are going to Europe for 2 1/2 weeks right as school ends. We feel bad because she works hard and she knows it will set her back. But the timing I think is the best. She'll have all summer and 4 more months to be ready for next season. Sports takes over our lives the entire year. I have 4 kids, all driven in their respective sports. But time away with family or whatever is essential. TOPs is a great program and making the team would have been cool but I wouldn't make it all that important.