In most cases, crashing a MyISAM table is nothing more than throwing mud on the MyISAM file header. It keeps a running count of the number of times the file has been opened. It increments upon opening and decrements upon closing.
You may want to look at the value for open-files-limit. This is an option that you cannot dynamically set with mysqld running. It can be configured at startup. What is interesting is its explanation in the MySQL Documentation:
Changes the number of file descriptors available to mysqld. You should
try increasing the value of this option if mysqld gives you the error
Too many open files. mysqld uses the option value to reserve
descriptors with setrlimit(). If the requested number of file
descriptors cannot be allocated, mysqld writes a warning to the error
mysqld may attempt to allocate more than the requested number of
descriptors (if they are available), using the values of
max_connections and table_open_cache to estimate whether more
descriptors will be needed.
By default, mysqld sets this values based on the OS and how many maximum open file handles mysqld believes the OS will give to it.
You can take a risk and raise that number in /etc/my.cnf and restart mysql. As mentioned in the MySQL Documentation, a warning will be posted.
Talk to your sysadmin to see if your OS can have its file handle limit raised.
Once you can get it raised, restart mysql and see if the open_files_limit was raised as well.