As technical analysis depends on indicators to predict the movement of a stock , why a particular indicator fails. a) after  some time of use in the market b) for particular stocks ?

Technical analysis based on the data points of a stock's price movement with time and volume. Hence the indicator you are using, it's giving the future prediction price based on the previous history of the market. Indicators are tools, so you need to understand the price action of stock with multiple time frames before you insert any indicator. I hope you can find every time the result will vary hence your future price too. You will get a better identification of price momentum.

Technical Indicators are not a tool used to buy and sell.
It acts as an additional confirmation for your method or strategy.
Note it's an additional confirmation.
The BEST indicator to use is PRICE.
Price is the best indicator, and then the Volume.
Before any indicator, price gives confirmation.
OPTION CHAIN will also give you an indication, better than any indicators.
Never Rely on Indicators.
If it were so easy to make money in the Stock Market, then 90 % + people wouldn't have lost money. ☺

The indicators are all lagging indicators. They give indication based on what price charts show. Technical analysis is never about catching the exact bottoms and top of a trend. Its about focussing on the entry and exit positions. So it can hapen at times that your indicators show buy but prices reverse. At that time, you have to use your stoploss which is again an essential thing taught in technical analysis. Even the best strategies and indicators dont’t have a 100% success rate. Prudency is in making use of that 70% or 80% hit rate as efficiently as possible. As a side note, technical indicators work relatively better in liquid stocks. So if you apply the technical studies on illiquid securities, they'll fail more often.

Depending on the major changes in the fundamentals of a company, the stock will move accordingly irrespective of technical data. I would always advise you to look at multiple factors and hedge your intraday or positional trades rather than taking one side views. In this way, even if your view goes wrong, your loss will be limited.

Indicators are Secondary derivatives of Price and Volume; primary is price & Volume themselves. That is where the beauty of Price action Trading Kicks in. Just by observing Price & Volume we can know when to enter the trade and when to exit the business etc. But to do this, one should have a keen ability to understand what happens behind the chart. Price action covers 80% of a good trading strategy if a person is good at analysing them.
Now Coming to Indicators, all Indicators works well when the person knows in and out of the system he is using. Let's Take RSI for example, many times RSI goes into Oversold or Overbought zones when the market is highly trending with significant momentum. An Average trader uses 14-day Default Settings. Still, who knows Price action trading, He knows the market is in good energy, so he adjusts the RSI for 20 or accordingly, it doesn't necessarily mean the market will come down, but the trader is very well aware how price wave functions consequently he takes the trade.