A way to permanently increase the number of hit points your Neopet has is to give them a special item such as Kauvara's Potion. Unfortunately these items are EXTREMLY rare and VEEEEERRRRRY expensive.
You may also raise your Neopet to higher hit points by going to the Healing Springs in Faerieland sometimes, but this will wear off after a while of battling & healing or if you go back to her or random events could restore your neopets HP back to Max. http://www.neopets.com/faerieland/springs.phtml
You could also complete quests given to you by the Dark Faerie in random events, NOT Jhudora. Sometimes the Faeries will set Quests for you. If you can bring them the items they want, they will bless your pet with new abilities and make them stronger. They are kinda rare though. http://www.neopets.com/quests.phtml
You can also try zapping your pet with the lab ray...but this is unpredictable and the whole lab map is quite a bit of NP. Each piece of the lab map range from 30,000 NP to 90,000 NP most of the time.
There are also Neggs & Shrooms, VERRRY expensive some raise HP.
Purple Spotted Shroom either heals 3 hitpoints, increases hitpoints by 1 or increases strength by 1.
Cool Negg increases Level by 1, hitpoints by 2-3, movement by 1-3 and strength by 2-3.
Super Negg increases Level by 1, hitpoints by 1-3 and movement by 1-3.
Faerie Queen Negg increases hitpoints by 1.
Snegg increases hitpoints by 1-3 and movement by 1-3.
Spiked Negg increases hitpoints by 2-5.
Another thing to try is going to Coltzan's Shrine everyday. Different times give you different things!
Endurance/HP: Every hour of the day
Speed: Every fifth second of the hour
Defense: Every tenth second of the hour
Strength: Every thirty minutes of the hour
Level: Every even (2, 4, 6 ...you know) hour of the day
Burnt Food: 11:00 - 12:00 NST
Dubloons: Every 55 seconds past the minute
10 Strength Points: Every 30 minutes past the hour (must be right to the second!)
http://www.neopets.com/desert/shrine.phtml
The best (but slowest) way to increase hit point/health level is training for endurance at Cap'n Threelegs' Swashbuckling Academy http://www.neopets.com/pirates/academy.phtml or Mystery Island Training School. http://www.neopets.com/island/training.phtml
I hope my answer helps you!