How can we persist the leds blinking rather than swithching from one led to other while using a demultiplexer
... its difficult to identify the LEDs that blinked.


If you mean that it is difficult to read them then no, it's not. Multiplexing is the standard technique used for LED seven-segment displays. Provided the blink rate is fast enough and intense enough the light will appear continuous to a (relatively) static observer.



Figure 1. A typical 50 mA LED (1) can be pulsed at 200 mA (2) for short duration (3). The note says 100 µs per 1000 µs.



Figure 2. Timing diagram for high-current driving of the LED.

Using the timing of Figure 2 the flicker will not be visible to a human eye.



Figure 3. For flicker-free displays a latch can be used. Source: LEDnique.

For further reading see the link above to a short article I wrote on the subject.