About 10 mobile phone towers have been destroyed since then.
The latest attack on a mobile phone tower came just before dawn on Saturday in the southern province of Kandahar, a mobile telephone company official said.
"During the day, we have problems with some Afghan forces who close down our operations because they say we shut down for the night," the official who declined to be named said.
The official said the network would continue to operate round the clock if they were guaranteed security and protection by Afghan forces.
Residents from parts of Kandahar and Helmand province in the south, as well as the northern provinces of Zabul and Ghazni, say their mobile telephones do not working at night.
The Taliban fighters, ousted from power in 2001, rely on mobile and satellite phones for communicating with each other and the media in their campaign to oust the pro- Western Afghan government.
Mobile phones are virtually the only means of communication in Afghanistan.
The four mobile phone operators in Afghanistan, three of which are foreign firms, have invested millions of dollars in the country since the removal of the Taliban.