Hello, my name isXXXXX and I have over 20 years of experience as a veterinarian. I am very sorry to hear about Zeus's grass eating and fluctuating appetite.
Dogs with nausea or gastroesophageal acid reflux often eat grass to make themselves vomit. They will often swallow repeatedly and lick things trying to soothe their nausea and acid burn. If they can rid themselves of whatever is irritating their stomach that way then all is good.
But when they are repeatedly eating grass and continue to be uncomfortable then we need to stop them from eating any more grass.
While stress could cause gastrointestinal upset in the short term it should not last this long. Dogs with ulcers won't have waxing and waning symptoms. They should have consistent symptoms.
Possible causes of nausea causing grass eating include a change in diet, dietary sensitivities or allergies, or eating things that they should not like too many fatty table scraps or garbage, bones etc. Because he's a younger pup metabolic organ failure (kidney or liver disease), pancreatitis, inflammatory bowel disease or even infiltrative cancers are possible causes but less likely.
Has he eaten anything he should not have recently (toy pieces, bones, garbage)?
Any changes in food or treats?
You can give him acid reducers to try and settle his stomach. Either:
1) Pepcid-ac (famotidine) at one 10mg tablet per 20 to 40 pounds of body weight every 12 hours.
2) Prilosec (omeprazole) at one 10mg tablet per 20 to 40 pounds of body weight every 24 hours.
These will reduce stomach acid and should help settle his stomach. These can be used long term if necessary as they are very safe.
I'd also pick up his food and water for now. A couple hours after the pepcid you can offer small amounts of water or ice cubes to lick.
No food for 24 hours. Small amounts of water only.
After his 24 hour food fast then start a bland diet of 1/3 boiled hamburger (or chicken) and 2/3 boiled rice. Give small meals several times a day. Feed the bland diet for several days, then start mixing in his regular diet and slowly convert him back.
So watch him for continued nausea even with the acid reducers, blood in his stool or vomit or a fever (more than 103.5F rectally), a tense painful belly or lack of appetite after his food fast. If any of those occur it is time to seek hands on veterinary care.
Since this has been a repeated problem for him consider whether he has been getting different treats or lots of table food, or have you been feeding a different diet?
If you go back to the original food and stop table food and treats and his nausea continues then you may wish to consider using a using a low irritant food, like Hills i/d or Purina Veterinary Diets EN, or a hypoallergenic food such as Hills z/d or Purina Veterinary Diets HA. He may have a dietary allergy or a sensitive stomach.
Please let me know if you have any further questions.