The best way to extend the range is to have two xBee’s act as a backbone. For example, I have a long driveway 1,200 feet and every Christmas I put direct attached hue bulbs at the end of it and shine them on a Merry Christmas sign. To extend the ZigBee network that far I use two xBee’s configured as outlined above. One xBee is close to the house but outside and it connects to the SmartThings hub inside in our basement. The other xBee is in a weather tight enclosure out at the end of the driveway. The two xBees (that are in line of sight) automatically connect to each other and extend the ZigBee network out to my Hue bulbs. Works like a champ very reliable. I would give that a try out to your shed. What type of device is in your shed that your trying to reach? Is it one of SmartThings presence sensors? If it is, they work best connected directly to the SmartThings hub.
You asked in an eMail if you can ping the xBee from SmartThings to see if it will respond. The technical answer is yes but you would have to write a custom device type and Smart App to do it. Digi’s xBees have proprietary cluster commands on end point 0x11 (if I recall correctly) and one of them loops back packets it receives. But instead of doing that use the XCTU program to map out your ZigBee network. It will show signal strength between all nodes and who is connected to who.
If this still doesn’t work I would entertain the possibility of radio interference either from your WiFi network or another close by ZigBee network. A quick test would be to see if things improve after you turn off all your WiFi hubs and routers. If it does you may want to change the channel of your WiFi network. Its pretty rare to have interference with your WiFi network but it is possible.