The low gear dogs in the transmission are strong, but the engagement mechanism is not well designed. If the shift cable is not properly adjusted, it can be driven without low gear being fully engaged which generally results in the dogs becoming rounded off and it will not engage low gear or will pop out of low. Usually, you can continue to ride in high gear until you can get it repaired. Learn about shift cable adjustment here.
For sub transmission rebuilding, we recommend contacting Adam Brown at AB Custom Fabrication and Rebuilds. He is the foremost expert in Honda sub transmissions and offered rebuild service for very reasonable prices and quick turnarounds. His last known price for a low gear rebuild is $400 plus return shipping ($75 flat rate). If you have damaged your reverse gear, he can repair that as well for a bit more. Upgraded CryoHeat parts are available for the ultimate "bulletproof" rebuild. You can find him through his Facebook page here: https://www.facebook.com/abcustomfabrication
Use different oil: from the factory Honda uses the same 10w30 oil that goes in the engine. AB Custom Fabrication recommends using Royal Purple 75w90 gear oil. Many owners also use a 1qt of 10w40 synthetic with 1/3 quart of Lucas Synthetic Oil Stabilizer. The oil is not shared with any other system, so you may safely use oils with moly in them as well.
Better oil goes a long way, but also DO NOT FORGET to keep your shift cable properly adjusted. See my page on Shift Cable Adjustment for more info.
Alternative shift gates are available with deeper slots cut that allow you to pull the shifter harder into low than the stock gate allows. If you don't want to put one of the inexpensive aftermarket gates, you can grind out the slot in the factory one a bit. Keep in mind, most dealers are rejecting warranty repairs on sub transmissions if the factory shift gate is not being used, so keep your factory one to swap back in if you are still under warranty.