IANAL, but from what I can gather (at least with the USPTO in the USA), a trademark can be weakened and even lost when not properly monitored and/or enforced. It would be unwise for any business to fail to protect their trademark(s).

(note: IANAL)

I don't know what country you're in, but they're in the US, and their lawyers are legally obligated to defend their trademarks against all violations, or they risk losing the trademark. So they will. Trademark use is by category, so you might be able to start a business called Quark Cupcakes, but you're both doing software, so it is a clear violation.

It is really hard to find a good name, and obviously it is your choice to stick with Quark. However, I do expect you'll get a cease and desist letter unless you change the name.

> Perhaps it's time for them to rethink their entire strategy.

Their strategy works. Yours is unproven.

Just an observation :P