BTW, Paul's suggestion saving using the TEE command is great, however, you might not find this command on older devices. If not, most telnet/console programs have some screen display "logging" feature. I.e. if your does, you might show the syslog and capture the screen output. (NB: setting terminal screen length to 0 can will avoid the need to "paginate" through a lengthly syslog.)
Also keep in mind, between the time you "show" and capture your syslog contents, when you resize it, some syslog data might be lost. That, though, might be avoided if you can send your device's syslog output to an external server too.
BTW, as to why the syslog output is likely cleared, well for starters, consider if you size the syslog smaller than it was. In such a case, if the new size cannot retain all its current data, data will be lost. Second, although programmatically, output might be retained when the syslog size is changed, it's generally easier to just drop the current memory allocation and resize it (also likely better since, as far as I know, IOS doesn't use a memory garbage collector). Lastly, as the (buffer) syslog uses a circular buffer, and older syslog data is routinely lost from it, the thinking might also be, if you want a more permanent recording of syslog data, it should be directed to an external log server.
