Hmm yes; that's right; but for solid-fuel hence fixed-burn time missiles like the SA-3, the burn would be fixed. I mean if you shoot at a slightly out of range target; would the missile glide on and still attempt to intercept it on momentum; or self-destructs as soon as it runs out of fuel? Heh, Quite a technical question, no?
For S-75 (SA-2) there was an internal clock for about 85 seconds. Please check the description of V-760 missile in the SA-2E topic (the time self destruction mechanizm is the same for all types I believe, just here it is a nuke, so have some "add-on"-s
).