Some reasonable advice. However, if the remote works from one area but not another then either it's weak OR something else is bothering the opener. Since you say that from the same spot you can OPEN the door but can not CLOSE the door then the signal from the remote is strong enough. UNLESS you have a weak battery and open it then immediately try to close it.
Now: Batteries are cheap enough and easily replaced. So give that a try. If it solves the problem then - well - problem solved. If not, it's not the antenna. If it receives a signal it receives a signal. Whether it's to open or close the door, the signal is the same. When it receives a signal it changes the position of the door. If it's open then it closes the door. If it's closed then it opens the door.
If you have a fairly new unit check to see if on the wall mounted button there's a button that looks like a lock. Press it once. Then test your door again. If it worked then chances are your unit was in some sort of lock mode. But that doesn't explain why it will open. Locks are supposed to prevent unauthorized opening.
Does the door operate normally when you push the wall button? If so then either the transmitter battery is weak (as already suggested) or there is something seriously wrong with your opener system.
You've checked the beams. Nothing blocking them. But if they fail, you CAN open the door but not close it. The only way to close the door when the beams have failed is to push the wall button and HOLD it while the door closes. Since I've never had that problem I don't know for sure whether you hold the button for five seconds (or something like that) OR have to hold the button until the door is fully closed. You'll have to read your manual for that.
As far as the antenna is concerned, the manufacturer knows what frequency the system works at. Knowing that frequency will determine the length of the antenna. Making it longer or shorter will weaken the signal, so don't waste your time trying to add wire to it and DON'T shorten it.
Finally, one answer suggested "massage the wire until it's straight." That will help ONLY if the wire is folded or wound up. As long as it is fairly straight it will work. Pointing straight down (or straight up) is the best way to get the most out of the antenna. An antenna that is pointed to one side will not work very well.
Finally, make sure the opener is properly grounded. A poor ground can affect how well the signal is received and interpreted.
Well, that's all I got. Hope this helped.
'')