Well this is really opinion-based. But there are some aspects to be aware of.
Some clients will see your failure to invoice as an "ok" to send you more changes then act shocked when you want to be paid. For this reason you need to be a bit careful with free services. Clients like this just try and roll over you and then start becoming very difficult when you do want to invoice.
Some clients will see the offer to not invoice as a great thing and it will merely improve your standing in their eyes. Clients such as these understand that whether or not to invoice is your choice and they never expect free services. So the occasional "That was a simple thing, no charge" will go a long way towards great customer service.
Then of course there's a range of clients in between these two types. Each leaning slightly one way or the other.
Whether or not completing something for free is a "good" or "bad" thing is highly dependent upon the actual client.
I often complete small, minor, inconsequential things fee of charge for my clients that are very good clients and never expect anything for free.
On the other hand, I have clients that any minor thing is invoiced for because if I fail to do that, they'll start sending repeated requests for "minor" things and these start to pile up taking more and more of my time.
However, I'm not referring to "1-2 hours" of work. I'm referring to 10-15 minutes of work. If it takes me 1-2 hours to do something, it's invoiced for in all instances. An hour spent completing that "minor" change is an hour I could have spent on another, paying, project. My time is a commodity. Do not sell yourself short. That 1-2 hours to "find the problem" is a direct result of your knowledge and experience and it is billable.
Theres a story that relates to this well....
A man takes his car to a mechanic because it's making a funny noise and running really rough.
The mechanic opens the hood, looks around for 5-10 minutes, pulls out a screwdriver and turns a screw. The noise stops and the car starts running as smooth as the day it was purchased.
The man is thrilled and says, "Fantastic. Thank you. What do I owe you?"
The mechanic goes over and fills out an invoice and hands it to the man.
He looks at the invoice and gasps, "$100!! How can you charge me $100 when it only took you 10 minutes??!!"
The mechanic replied, "Oh, sorry. Here let me itemize that for you." He then takes the invoice from the man scribbles something on it and hands it back tohim.
The invoice now reads....
Turning Screw ...................$5
Knowing which screw to turn.....$95
Total Due ......................$100.
Do not sell your knowledge and experience short.
I look at it this way... Imagine I charge $100/hr. So 15 minutes is worth $25.00.
It takes me 15 minutes to fill out and send an invoice. So really I make $0 if I invoice for 15 minutes. Actually factor in dealing with the check/online payment etc, I probably lose money if I invoice for 15 minutes. Therefore its not really financially worth my time to invoice for 15 minutes. It may be worth it to invoice just to send a message to the client that "everything" is billable. But if a client already understands that, the message isn't needed.
However, I make $75 if I invoice for 1 hour. If I were walking down the street and saw $75 lying on the ground, would I ignore it?? Uhm.. no. So why would I fail to ignore money owed to me. If I stand to gain financially from any invoice, the invoice is sent.