I paid to have my transmission repaired and it has been to the shop 4 times in 7 months. Can the repair shop be liable for my rental car expenses?

Possibly; however, you would need to show that either the shop is negligent (or not performing to accepted reapir show standards) in not making the repairs, or that they are deliberately defrauding you (e.g. by claiming to repair when they do not). If it's merely the case that your car has a very bad, intractable problem, then no--the repair shop would not be responsible unless they had actually warranteed their work. Without a warranty, service and repair people are responsible only for careless or deliberate wrongdoing, not for simply being unable to fix a major problem.