Fares generally do not increase over the course of a day. There are different fare categories or buckets that have fares available at different prices. Southwest used to show all buckets. Now, the "wanna-get-away" fares lump all the restriced buckets together and only display the lowest fare available for your party size. So technically the fares don't go up - the cheap ones sell out. Ususally the fares and buckets are adjusted at the most daily but more probably weekly.
I have also seen where you can get one seat at a good price but when you search for three you cant get that price. Same reason, not three low fares available. I have actually booked separate tickets to take advantage of this. Does not happen all the time but it happens.
My rule of thumb is book immediatly after fares are released or wait a few weeks for the dust to settle.