Does input offset voltage for amplifiers remain almost same
It should be fairly stable for a given chip, when measured at the same temperature, supply voltage and common-mode voltage (and assuming the chip is not damaged by overheating, electrical transients etc.). There will be some drift over time, but it should not be large for most op-amps. Some early CMOS-input op-amps had significant long term drift if they were exposed to large differential voltages, but that's more the exception then the rule. 

At different temperatures, the offset voltage will be different, and the limits on that change are usually specified by a parameter such as TCVos, in microvolts per Kelvin. 

Here are some specs for a typical precision op-amp (OPA177): 





Here they specify the long term drift as typical 0.4uV/month, the maximum Vos over the entire temperature range and the maximum/typical drift with temperature. 

The temperature drift spec is usually done using the 'box' method, where an imaginary box drawn around the offset voltage graph from -40 degrees C to 85 degrees C has a height that is not to exceed 150uV, which represents 1.2uV/degree C. The total offset must not exceed +/-100uV at any point in that range and the offset at room temperature must not exceed +/-60uV. In practice the curve will be smooth and often will be monotonic. Note that there is no guarantee that the slope of the curve will not exceed +/-1.2uV degree C, only the average over the whole temperature range is guaranteed. 

Cheap general purpose op-amps will have much larger offsets and drifts, and often the drift with temperature and time is not specified, but the principle is the same. Typically the larger the initial offset voltage of an untrimmed op-amp the larger the drift with temperature will be.