It is a custom and tradition for Hindu Temples to be closed during an eclipse.  Why is that?

Hindus believe the eclipse be it lunar or solar to be impure or spoiled. An eclipse concerns a duration of time when the rays of the great cosmic lights are blocked and cannot reach the earth and its inhabitants.  Thus the effect of the eclipse falls on all living organisms including human beings, animals, birds and even insects. When the eclipse or grahana occurs in moon or sun, which  provide energy and light to this earth it is considered a bad day for the earth and  the living. The eclipse period is therefore considered an inauspicious time. This is called Sutak kaal. It is a time when no auspicious work should be done or no worshipping  or praying or visiting the temples can be carried out. Temples are however immediately opened once the eclipse is over.

It is believed that during the solar eclipse in particular, there is a strong negative charge loading on the earth.  Since the temples are built to attract astral energy and  positively charge the devotees, the positive effects will be reversed during the solar eclipse. This is one way of thought. Another way of thought is that temple deities, which have been consecrated by mantras and rituals, have an external energy field around their forms, which combined pull of the sun and moon during the installation can weaken during the eclipse. Deities in the temples are installed by avaahana mantras. The effect of such beejamantras may diminish during the eclipse, if the deity is exposed and therefore the temples are closed. In some circles there is a belief that astrologically those born under the signs of Scorpio and Sagittarius should donate items during a lunar eclipse to get rid of any ill effects.

Are there any exceptions to the rule?

Yes.

The Tiruvarpu Sri Krishna Swamy temple near Kottayam, Kerala is an exception to this practice. The 1500 year old temple is the only Mahakshetra in India which doesn't close its door during an eclipse. The practice of not closing the temple during an eclipse is associated with a centuries old temple legend. The presiding deity of this temple is Sri Krishna in form of Balamukunda. The installed deity is of the hungry form of Sri Krishna after the slaying of Kamsa. At this temple the doors were originally closed during an eclipse but they found that when the doors were opened the waist belt of the Lord Krishna has slipped down and this  was because Balamukunda became very hungry and his stomach had flattened. From then on, they stopped closing the temple during eclipse.  This temple opens the earliest of the temples in India. At 2.00am the main doors open and around 2.40 am the deity is offered the first nivedyam. It is widely believed that the deity cannot tolerate hunger and everything else including important time based rituals therefore takes the secondary position.