Neither of these two claims is true, or at least real trends were more complex.

• The biggest drop for the Greens was before getting into government, and that due to internal conflict (over calling for 5-DM-a-litre petrol prices): from highs of 12% to a 1998 election result of 6.7%.
  
• Through most of Schröder's first term (that's during the Kosovo participation and before Agenda 2010 and Harz IV), the Greens struggled, but started to rise towards the end and significantly improved their result in the 2002 elections to 8.6%.
  
• Throughout Schröder's second term, the Greens polled higher than their 2002 election result and did well in regional elections. They fell down in the last weeks of the 2005 election campaign (ending up at 8.1%), due to a last-minute SPD surge to prevent a CDU-FDP government.
  
• During the Grand Coalition era, all the hype was about the Left Party. The numbers for the Greens fluctuated, and even with gains to 10.7%, they stayed smallest parliamentary party as the Left Party and the FDP gained more.