2012 Honda Fit LX. We are having trouble starting our car in the mornings, it needed a new battery so we installed a new battery about 2 months ago, But the car is still having trouble starting in the mornings only.
Have notice the battery is loosing Voltage when the car sits overnight.


Any suggestions?

 

If you suspect the battery is draining hook a current meter/probe up to it and see how much is draining. Then start disconecting things and removing relays until the draw goes away.

Was anything recently installed? Does it have anything that is aftermarket.

 

nothing recently installed, nothing aftermarket. we bought the car in 2012, this is the first issue we have had with it,

 

Just to be clear, you're saying that the FIT is behaving like the battery is drained down and that apparent condition is what you believe is making it hard to start because the starter isn't turning the engine over fast enough, versus, good turning over speed by the starter but the engine just isn't catching / firing ?

 

I think it could be one or a combination of a few typical issues with cars in general.

1- Some parasitic power draw as noted by @GolNat
2- The main power and grounds are not working proplerly (corrision, bad contacts, damage)
3- The starter motor is having issues
3- The alternator is not charging the battery properly anymore
4- The battery is bad (did you have same problem the week after installing new battery?)

The first two can be checked DIY with the help of a few youtube videos and a basic multimeter. Use goggles and extreme caution as you don't want a major shock to your body or damage to the electronics or explosion of the battery.

The last three can be checked by your mechanic or typical chain parts stores.

 

Since a new battery has recently been installed, my purely speculative guess is something wasn't connected right.
If you're not a D.I.Y. er, stop by a auto parts store and have them check the connection terminals, tighten if necessary. Most auto parts places can also check the charge.
Neither things might be the problem, but it's the cheapest, easiest place to start.