If a diode is operated in breakdown region and if it is used again will it lose its characteristics or work normally?
Breakdown itself does not damage a diode, if the current is limited. Zener diodes constantly work in this mode.
What is important is that if there is no current limiting, the diode will heat until it would burn, and you'll have a short circuit or open circuit, and it won't work.
zener breakdown is different from avalanche breakdown in the sense that zener breakdown occurs in heavily doped diodes where the depletion region is very narrow, therefore a comparatively small reverse voltage is sufficient to start conduction, whereas normal diodes are lightly doped thereby the depletion region is very wide, so a very high reverse voltage is necessary to start conduction. But remember one thing that this conduction in both cases occurs because electrons get highly accelerated and knock off electrons from other atoms therby creating more electron ion pairs