Until the early-mid 70's, Sunn marketed their amps as a head/speaker cab matched set. They didn't sell amps or cabs "ala carte". You could but an extension speaker cab seperate, but all heads came with a cabinet.
The Sonic l is a 2 X EL34 40 watt amp that was originally paired with a 1X15 enclosure loaded with a JBL D130, meant to do multiple duty as a guitar, keyboard, or bass amp. The Sonic l-40 is the same amp head paired with same enclosure but loaded with a JBL D140 instead, and was meant for bass.
Regardless, it should hold together until 7 or so, not breakup at 3.
The problem you are having is most likely, or at least compounded by, old leaky filter capacitors. They can't be good if they are original - they are 40 yrs old. Bad filter caps or bad tubes will both cause the problem you are describing.
Don't dump the old power tubes until you test them on an accurate tube tester, they may be worth something if they have any life left in them.
But.....It's 40 watts, not 60. It won't keep up in a loud band no matter what you or a tech might do to it.
If you want to learn tubes, surf and read, there is a lot of stuff out there. Some on the mark, and a bunch of "urban legends".
Find the book (yes, BOOK, like in school) "Beginner's Guide to Tube Audio Design" by Bruce Rozenblit. It will give you the knowledge of which you seek, and it's pretty user friendly. Just go slow and keep a calculator and note pad handy. If it where easy, everybody would be an expert.
Of course, if you read the posts on this and most other music forums, everybody already IS an expert!