Check the lengths that the timelines display for-it may be resetting it back to 0 weeks; just set it to show all (or whatever the equivalent is) and it should work.
If I click the Show All button, the timeline graphs appear normal up to a particular point and then everything plummets to zero from that point on. Setting the turn limit to anything up to 52 weeks results in an empty timeline. When I begin a game session and click the Turn button, the graphs lines temporarily go from zero to the appropriate statistic and then continue normally from the third turn on. But, when I end the session and get back into GalCiv2, the graphs are all zero again and all data from the previous session is missing. Interestingly, the comparison charts on the next from page -- where you can compare your race's Military, Treasury, etc. level with other races' -- appear okay, but the timeline graphs are useless. It is like the timelines just up and quit after a certain point.