Why can't the levator muscle be strengthened with exercise like any other muscle?

The levator muscle is one of two muscles which elevate the eyelid. Ptosis may be due to poor connections of the levator muscle to the eyelid. There are several other causes as well which can be evaluated in person by an oculoplastic surgeon. 

Ptosis usually occurs because of a separation between the tendinous insertion of the muscle and the eyelid soft tissue. Under these circumstances, strengthening the muscle would have no impact upon the ptosis. For this reason, the vast majority of patients with clinically significant eyelid ptosis require surgery to treat the problem.

The main reason for eyelid ptosis is that the attachment of the levator muscle/tendon to the eyelid loosens (and the eyelid drops), so strengthening the muscle, even if possible, won't be useful.  Moreover, it is a special muscle that is working and lifting the eyelid ~15,000 per day, so it is already doing the best it can to keep in shape!  Further exercise won't help. Luckily, the muscle can be tightened/advanced (ptosis surgery) in order to help lift the eyelid. See an oculoplastic surgeon for consideration.

In most cases of eyelid ptosis, levator muscle weakness is not the problem. The problem is the fact that the muscle attachment to the eyelid has slipped and that no matter how strongly it contracts, it will not fully lift the eyelid.

I can make this analogy:  lets say you have a hugely powerful bicep muscle. but if your hand isn't holding onto the weight, no matter how much the muscle contracts, the weight isn't going to be lifted off the floor.  Same thing with levator muscle and the eyelid.

Hope that helps

Blepharoptosis, or eyelid sagging has many causes. If the problem were as simple as the muscle being weak, then exercise would help. Problems with the nerve, the muscle, the muscles attachment and restriction by surrounding tissues can all play a part. A proper diagnosis is key to the proper treatment. Seek a qualified surgeon with experience for an evaluation.