Intermittently losing power in one leg of a Zinsco Panel
First off, look at your weatherhead.  That funny little gooseneck the powerlines go to. There's a crimp there on each wire.  The crimp, and everything between the crimp and the pole, is the power company's bailiwick.

You can't really measure there, but you can measure at the top (line side) of the main breaker. 

Turn off the main breaker to prevent crosstalk and feedback from influencing results.   Now measure 


From Hot L1 to Hot L2 (should be 240V)
From Hot L1 to Neutral (should be 120V)
From Hot L2 to Neutral (should be 120V)


If that is solid, then turn your main breaker back on, and turn off all breakers that are 240V, or handle-tied, or have a red wire going to them.  (Zinsco is unique in that a "duplex" double-stuff breaker can actually be a 240V breaker; that is the only panel capable of that trick.)  240V loads will contaminate test results, because they are a resistance between the two poles.  

Now, check the numbers again.  

If you see the 240V number being less than 240V, that is a lost hot wire.  If you see any 120V numbers being above 120V, that is a lost neutral.  You can limp along with a lost hot, but a lost neutral is a true emergency.   Turn everything off ASAP! 

If you see any lost wires, call the power company and report an outage.  

We have field reports of the power company discouraging people from reporting outages, by cross-examining you with questions like "Do your lights work"; their job is to screen stupid people to avoid false service calls.  If the above tests prove an outage, then you need to "lie" your way past the gatekeeper and get the truck out there.  It's not a lie: the outage is real, it really is in their bailiwick, and your lights really are out because you tripped the breakers to prevent damage. 

When the truck is out, be sure to point out this damage  you show here.  I have a feeling the pole-top splice may be in equally deplorable condition, and if it looks bad, the lineman could potentially fix it, call the job done and drive away, leaving this one unnoticed.  Don't let that happen.  Meanwhile stay away from it.