Hello, my name is***** and I have over 20 years of experience as a veterinarian. I am sorry to hear that Shadow has been vomiting intermittently for the past week.
The short answer is yes, you should be worried.
In many cases vomiting is triggered by eating something they should not, too much table food, too many treats or something they find outdoors, or esophageal reflux. These simple causes seem to come and go within 24-48 hours.
More serious causes of vomiting include viral or bacterial infections, chronic pancreatitis, a dietary allergy or sensitivity, inflammatory bowel disease, internal organ failure (kidney or liver disease), pancreatitis, a full or partial gastrointestinal obstruction or even infiltrative cancers such as lymphoma.
Rarely a parasite called a stomach worm (Physaloptera) can lead to intermittent vomiting. These are difficult to diagnose because they rarely shed eggs, so we can try simply worming her with a gentle wormer called Pyrantel and see if that helps. This is easy to do and inexpensive so well worth trying.
If that doesn't work and since he seems to feel well otherwise some dogs seem to vomit more on an empty stomach so feeding him small meals several times a day, and maybe a snack before bedtime, may be very helpful.
It may also be helpful to put him on an acid reducing medication as too much stomach acid, especially on an empty stomach, is very irritating and predisposes to vomiting.
I recommend giving him a dose before bed so that it is in his system in the morning when his stomach is most empty. You can give either:
1) Pepcid ac (famotidine) at a dose of one 10mg tablet per 20 to 40 pounds of body weight every 12 hours
2) Prilosec (omeprazole) at a dose of one 20mg tablet per 40 to 80 pounds of body weight every 24 hours
These are both acid reducers and should help him feel better. They are quite safe and can be used long term if necessary.
You might also consider feeding a low residue, low irritant easy to digest food. Both Science Diet and Royal Canin make sensitive stomach formulas you can find at the pet store.
If he continues to vomit even with the acid reducers, runs a fever (more than 103F rectally), has a tense painful belly or if he refuses to eat he should see a veterinarian for an examination, and some diagnostic testing. I would start with a complete blood count and biochemistry profile, a specific test for pancreatitis called canine specific pancreatic lipase, as well as fecal checks for parasites.
Please let me know if you have other details or a particular question based upon my response.