There are a number of factors that influence how long a glue board will be effective at catching bed bugs. When new they work very well but age, UV damage, dirt, and the severity of the infestation play a role in their longevity.
I have noted that glue boards exposed directly to sunlight turn yellow and lose their stickiness quickly. As such a sunny bedroom should always have covered glue boards. A dirty home will load the glue board with dirt very fast. It is entirely possible to ruin a glue board within a day of installation with dirt fouling. And severe infestations can trap hundreds of bugs per day which, in turn, requires more frequent changing of glue boards.
I did leave a glue board on a shelf (protected from floor dirt) for 3 months and noted there was a small layer of dust in the glue. I figured this glue board had about half the stickness of a new glue board. On another occassion I had a glue board in a home for 5 months (trap with 1 foot square dust shield) and it seemed to be roughly comparable to the 3 month old trap that was on the shelf. I considered both of these traps to be inadequate for the task.
The ideal method is to change the glue boards every two weeks but, if the home is very clean and the traps are covered, I think 4 weeks are ok. But this assumes no UV degradation from sunlight. I have seen 30 days of sunlight render glue boards utterly useless.
In practice it is rare to have a home that is clean enough to make the glue boards last 6 weeks. There is always some level of dust blowing about the cleanest home that will foul the glue.