It's actually castellated nut, but never mind.
The nut is castled so that it can be held in place with more often than not a split pin, though on very large nuts it will possibly be another bolt and castle nut, with a split pin, and so it goes on.
If it requires locking in place, then it should be.
If the manufacturer has designed this with a castle nut, then it obviously needs it else they would have saved a few pence and used a normal one.
As has been asked, is the cylinder cross drilled?
If not, don't just cross drill it, as you will create a stress raising point.
If the cylinder is not cross drilled, has it been replaced for one which is not, remember the rod could have been replaced during overhaul.
If the rod has not been replaced, has the nut been swapped to a castle from a normal by mistake, or because it was all that was available?
If it is a hydraulic machine then it will vibrate, it's just the level of vibration that will vary! ;)
Now Matt16, you are saying that there is a lot of strain on the threaded rod end, is this due to misalignment, or is it just heavily loaded?
A cylinder rod will always flex, it is just the magnitude that varies.
Where is the play, is it in the cylinder neck end cap, the rod end attachment, or the cylinder base cap mounting, it could be a trunnion mount or many others, but, what I am getting at is where the play is, rod attachment, body attachment or between the two?
Why is there excessive loading on the cylinder, is it being operated beyond its design limits, are you deliberately overloading the machine?
If the loads and forces on the machine are within design & operational parameters, then no matter how large they are, they are not excessive.
One final thought, is that there are other methods of preventing threaded fasteners from loosening. Has there been a formal recorded modification that no longer requires the securing device to the castle nut, but still allows the castle nut to be used?
It is possible, and as a retrofit, it would actually be cheaper to re-use thh castle nut, than replace it, if you went over to an alternative method of securing the attachment.
I would not weld the nut on, as the cylinder rod material may well not take kindly to the localised heating and rapid cooling of a weld, metallurgically speaking as it were, you could have an adverse affect on the properties of the rod. The nut could also be a free cutting leaded steel, which does not weld well.