As you can read in the mentioned article, the vaccination there only helps against one of 8 (since 2013 one of 9) kinds of botulism bacteria.
If you are certain it was bacteria-caused botulism, you can now assume which of them causes the botulism of you rabbit, and the other 7 (8) can cause a new botulism on the same rabbit.
Another uncertainty is: The immune system of your rabbit only acts against the bacteria. It cannot act again the toxic substance itself, I think. If your rabbit eats food with toxins of this bacteria again, it will get ill again. (There may not come "new" additional toxins, because the immune system kills the source bacteria, but they made an amount toxins in the food before it got eaten).
To the question, if it causes a life long immunity... This depends on a lot of circumstances. It is not linearly connected with the power of immune response.
Here is some new, additional information from lila's comments:
It makes sense that the vaccine isn't against the bacterium itself because these bacteria aren't even able to survive in our digestive tracts - and they need to be alive to produce the toxin: our natural intestinal flora and secreted bile acids make it impossible for these bacteria to colonize our digestive tracts and poison us from there. For example, honey sometimes contains spores of Clostridium botulinum (spores are dormant forms of bacteria, a bit like bacterial "seeds"), but it doesn't contain the botulinum toxin and it is safe to consume (with an exception of children less than 12 months old - digestive tracts of newborns are sterile and they need some time, which is up to a few months, to fully establish the natural intestinal flora; this is why it is bad to feed honey to children less than 12 months old, botulinum bacteria having much less or completely no competition from the infant's bacterial flora could colonize their intestines and poison them).
I have read some sources and I see that all toxins for which you could vaccinate are protein-based toxins. Proteins are gigantic molecules; for example, the chemical formula of botulinum toxin is C₆₇₆₀H₁₀₄₄₇N₁₇₄₃O₂₀₁₀S₃₂; such huge molecules don't really act like small molecules anymore, but more like complex, nano-scale objects or machines. Unlike bacteria, they aren't actual living organisms - but they are so large and complex that our immune system is still able to uniquely recognize them and respond to them as well. If we devastate these "machines" by messing up their delicate structure (technical term for this is protein denaturation), then they aren't able to harm us anymore - but they are still recognized by our immune system. Such non-harmful forms of toxins are called toxoids.
Botulism vaccine contains such "wrecked and non-working machines" - botulinum toxin molecules that have had their structure completely messed up by formalin - for our immune system to safely see, prepare the response and get ready to fight in case of the harmful, functional "machines" (active, dangerous toxin molecules) being in our system.