New member with questions

My name is Tom Lewis, I live in Carlsbad NM. I am a retired teacher and have made hand made knives for 40 years.

I have a Gamo 21 .177 air rifle with a Leapers scope. When I sight it in it holds 1/4" groups at 30 feet. The problem is when I leave it for a week or so and then shoot it, it is off a couple of inches at 30 feet. It doesn't seem to hold it's accuracy. I have tightened all the screws and bolts.

Any ideas and suggestions will be appreciated. 
 
Welcome to the madness/sickness/addiction. ;^) Spring guns are very hard on scopes and I have had one gun, a Diana 45, thrash six scopes in fairly short order.

You may want to make sure your barrel is clean and check this on your scope.

https://www.airgunnation.com/topic/groups-moving-around-maybe-your-scope-is-the-problem/

Then think about a better mount for the scope.

https://www.pyramydair.com/s/a/Bullseye_ZR_1_Pc_Mount_Fits_1_and_30mm_tubes_11mm_Dovetail_0_04_Droop_Compensation_Recoil_Compensation/5495

I have one on my Diana 54 and it shoots lights out.

https://www.airgunnation.com/topic/shot-some-targets-50-yards-with-the-diana-54/
 
If you don’t have a quality springer scope on it, that could be a problem. But I will say that I have noticed your issue with my springers with good scopes. I was shooting my TX200 the other day, haven’t touched it in months. It was shooting left and a little crazy. From past experience I didn’t hurry up and start clicking my scope. I just kept shooting and things got better. Wound up only going 2 clicks right. It’s almost like they need warmed up if they haven’t been shot in a while.
 
Thanks for the advice and suggestions.

I have checked the screws they are all tight. 

It may be that the gun needs to be fired several times before it will hit the bulls eye, but when I want to shoot a pest in the yard this is not practical. I used to have a Dana springer and it was always accurate. Maybe I need to get another one. 

Thanks again for all the responses. 
 
True, the Gamo is not of the same quality as your old Diana, and the cheap scopes included with inexpensive rifles aren’t known for their ruggedness. 

Good spring guns are another story. Some years ago I sold my old TX200, which I’d used in FT competition, to a friend. Five years ago I bought it back after he complained that he could never hit anything with it. Last year I spotted a rat in my garden, about 20 yards away. I grabbed the TX200, put a pellet in, and guessing my friend hadn’t touched the scope, held on the rat’s head. Pop. Dead center.