In the days when mainframe computers used tape as a long-term storage medium we used to completely wind and rewind all our tapes at regular intervals. This was to keep the backing flexible and stop the layers of tape sticking to each other. Failing to do this could result in the tape becoming useless - the tape could break or the oxide layer, used to hold the data, would crack off the plastic backing not only losing the data off the tape but also clogging up the tape heads on the computer. We also made more than one copy of each tape.
Video tapes are no different - it could be that your tapes have got into such a state that, in effect, the data will fall off them when you try to read them.
Please heed the warning and always keep at least one copy of any important data on your computer and regularly check that CDs and DVDs etc are still in good condition - they do deteriorate with time, so it's never a bad idea to just copy them every 5 years or so.