This is very far from idea. In fact, it can damage your database file. If twould appear that it is already damaged given the crashes and you should run a recover on your file to check for such damage.
The file should be placed on a computer where you have FileMaker Pro installed. The copy of FileMaker on that one computer should be used to open the file to host it over the network. Other users should then use Open Remote to find and open the file.
PS. You might check to see if FileMaker Inc still has their "gift in kind" program going and whether your organization qualifies. You might be able to get some free software through that program if it still exists and if you qualify.
The database shouldn't really be on a shared network drive, which lead me to another question. Are you using Filemaker to host the database and then using "Open remote" from the other computers running Filemaker? If not, that is the cause of your problem.
See the following links about sharing your file http://www.filemaker.com/search/index.html?cx=017511444758876863470%3Acq2n1yrh6e0&cof=FORID%3A10%3BNB%3A1&ie=UTF-8&q=sharing+file&sa=Search&siteurl=www.filemaker.com%2Fsearch%2Findex.html%3Fq%3Drelationship%26cx%3D017511444758876863470%253Acq2n1yrh6e0%26cof%3DFORID%253A10%253BNB%253A1%26ie%3DUTF-8%26sa%3DSearch%2523911&ref=www.filemaker.com%2F&ss=2343j732247j12
Thank you very much to the two who responded to my post. We've fixed the issue and hope for smooth sailing now for our Veterans!