Battery Dead problems of the 2008 Cadillac SRX

While on trip to texas, we were starting to enter freeway from rest stop near slidell la, as we were accelerating engine died leaving us with no power brakes or power steering. Managed to pull car off road. After 5-10 minutes tried starting car, engine fired uo ok so commenced trip. Shortly after that all instrument gauges quit, pulled off highway to check engine, all ok so started on. Stopped at Cadillac dealer in baton rouge, they could not find problem. Gauges stopped working several more times but no engine problems. Arrived in texas no further problems, however next moring car would not start, battery dead, called Cadillac dealer (car was lease) they came out and replaced battery . Next day car stopped running while in traffic, again after 5 minutes was able to startup again. Took car in to dealer in grapevine texas they were unable to duplicate problem. Several weeks later, battery died again, plano Cadillac dealer sent out technician and replaced battery again. These problems continued until we came back to our home in alabama. Same problems on that trip. Took car into dealer in mobile alabama were we had leased car and told them to fix it, replace it or keep it under state lemon law.