This issue has been persisting from the day I got the car so like 2/3 months back. It is a very intermittent issue as I can drive for hours and second gear engages fine but at times I shift into second (upshift or downshift) and it doesn't engage properly and its still in neutral even though the shifter is in second.

At a point I did believe that it was my fault but after getting the car back from my mechanic due to an ECU issue, I started focusing more on shifting into second just to make sure if its me or the car. But the problem is still there, drove for an hour and a half and at the end of the drive home, second gear didn't engage properly about three times. I'm 100% sure that its not from my end as I'm shifting properly. My mechanic did mention that their is an engine mount that's looking worn located more at the back of the engine as he explained. Could a worn mount be causing these issues? Keep in mind the car is quite low and our roads here for the most part are pretty bumpy.

Second gear itself when it engages which is most of the time feels fine and we did test for clutch slippage and everything was fine. Any ideas on this matter would be appreciated.

 

So honestly...... No idea what engine, car, or transmission you have.
But that would be some info that would make it many times easier for people here to awnser your questions.

I'm in an old 92 hatch not a stock engine or transmission and in my experience you can easily feel the gear "pop in fully" when you shift before you let up on the clutch.

Though sometimes when not moving and trying to shift between first and reverse, I get some resistance, and can easily feel it not wanting to engage. I'm a gentleman and don't force stuff so:
Generally, without letting up on the clutch, quickly sliding it fully into second, then into first or reverse seems to line crap up and make the magic happen.

In these situations you might try holding the clutch, sliding it fully into 3rd then back to 2. As a temporary work around. ( I've heard these called manuals with "personality" and is why people never let others drive thier cars.)

Now, a while back I did change the CVs and that required me to change the transmission oil/fluid. After doing so, shifting was allot smoother! Still have the occasional hiccup between 1st and reverse, but not nearly as often. So that would be a great place to start.
I did use OEM Honda manual transmission fluid. I dunno if that made a difference. But that's what I did, and it did help.
GL!