Why does a comet lose its tail permanently?

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I know that a comet often has a nuclea and a very long tail. the gravitation force of the core on the tail particles must be very weak and they will not have opportunity to come back to the core. So consequently, the comet will decay over time won't it? Is that right?
 

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Yes. The mass of a comet will decrease over time. The 'Active area' of a comet describes that which emits gas and dust and since these gases and dust are effectively lost, (i.e. the mass decreases) the active area moves around since the comet changes shape/size. Normally, I think it is believed that the active area's do not exist forever since a layer of dust will build up and cover - drowning out the melting effect of the solar heat. Other regions of the comet may become active instead.