The room where I work and usually sync is actually further away from the main router than where my phone usually sits. My wireless printer is also in that room and I have no problems syncing it or anything else--only Evernote. If my phone is with me away from my home, but I have updated my computer, it will not sync to my phone, even though the phone is connected via cellular or another WIFI connection.
For example--if I put a list together of things I need to pick up from the store, I used to be able to create the list on my computer (even the night before), and it would be on my phone when I got to the store. But not now. If I don't remember to put my phone closer to my computer after I update the list (or any note), it will not sync. I have OFTEN arrived at the store thinking my list would have automatically synced to my phone, only to find that my list is not there.
But as soon as I go back home and put the phone near my computer, it syncs without a problem. It's frustrating and annoying, to say the least.
Thanks for your questions/clarifications. But I don't think the WIFI strength is the issue. The WIFI signal in our home extends out into the yard. (And I have an Airport express in tandem with the Airport Extreme. The express is in the room where I usually work and the phone is in the adjacent room--with no wall between.)