The main reason why a government would not want to use fiscal policy to close a contractionary gap is because the use of fiscal policy to do this might well cause excessively high government deficits.

If a country has a contractionary gap, the government would have to increase its spending and/or decrease its taxes.  If the government were to do this, it would incur deficits.  This can be seen in what happened with President Obama’s stimulus package in 2009.  The government tried to lower taxes and increase spending.  When it did this, it ran a deficit of over $1 trillion. 

Governments will often not want to do this.  It can end up being bad for their economy in the long term as their debt increases.  Therefore, governments might not want to use expansionary fiscal policy to close a contractionary gap.