Sorry if this has already been posted (or is just obvious) but there's so many threads right now it's hard to keep track of what's been said. I came across a site/blog which had some good advice for increasing the range for remote play and it worked for me (sorry I don't have the link/remember the name so I can't give credit for it) so I thought I should share it.

First, on the PS4 enable the setting that allows the PS4 and Vita to connect directly. Then take note of what channel your wireless router (or neighbors routers too if you're in an apartment building) is on. Then go into your Vita network settings and change the ad hoc channel to something that is different from your router.

Before my vita was on "auto" (the default setting) and the router was on 11. Basically I just changed my Vita to channel 6 and it significantly increased my range since they should now no longer be interfering with each other. Last night I was playing with a nearly flawless connection in a room where previously it couldn't even locate the PS4.

Anyway, this might be obvious to people here (most seem way more tech savvy than me) but I figured some other people like myself might not know about it. Though I should add a disclaimer that I'm not guaranteeing this will work for anyone, it just did for me so I assume it would for at least some others as well.