Interesting questions, Paula, because it gets at so much that is fundamental to how capitalism works. The answer to the first one is no, in this sense. At a minimum, capitalism requires the *expectation* of profits. Each capitalist advances money to produce a product or service, which she sells for more than it cost (i.e., the money advanced to pay workers and replenish plant and equipment). The difference between price and cost is profit. There is no reason for the capitalist to do that if she didn't expect to have more money after a production round than she started with. There is no such thing as "nonprofit" capitalism. Profits are the purpose of capitalism.
OK, but what if capitalists expect profits but don't get any, maybe for quite a while? And let's assume they still expect to get some in the future. Is that sustainable; as you suggest--can you just replace assets and keep going? Not really. To start with, we have to be careful about some defintions. First a correction. Asset replacement doesn't come out of profits. It's a cost of business (depreciation), just like wages, that must be covered before any profit is received. You have to pay workers enough so they don't starve and replace used up equipment, then you start earning profits.
One purpose of profits is to provide money to expand production, to pave the way for greater profits down the road. Is this necessary? Well it is possible to conceive of a capitalism without growth. John Stuart Mill, pre-Marx, in fact, had a theory about the "stationary state", which he thought of as kind of a paradise after a certain amount of abundance was achieved (he was worried about many of the negative effects of capitalism, and this fantasy about the future allowed him some comfort). We have, of course, far exceeded the abundance he was thinking about, and, needless to say, that paradise has eluded us.
It's easy to see why. You can't ignore the lust of capitalists for more. Capitalists keeping putting their money back into another round of production because they want still more money at the end. A Marxist would say the essence of capital is self-expanding value. Each capitalist doesn't succeed, of course, and sometimes as a class they run into dry spells, as Doug mentioned in Japan. But each has to try. The compettion between capitals means that someone who isn't trying to expand will get eaten up by others who are. Mills didn't understand this. The stationary state will never get here.
So that's one answer to your questions. A profitless capitalism can't be the plan.
But, you may ask, if capitalists really try to reinvest (accumulate) everything they can get their hands on, why do we see so many high living, fat, rich ones? You'd be right; nowadays capitalists as a class generally make one major exception to this general rule. First they pay themselves fat salaries, plus stock options as claims on future profits, have fancy offices, expense accounts, etc., and *then* they accumulate everything they can get their hands on. They have mucho discretion as to how much they give themselves, and to top it off, their salaries and related benefits show up as employee compensation in the national product accounts. Before profits are even calculated. In short, this is one of the reasons that what you see as "profits" in the accounts often doesn't help you understand much. It's only a part of the money available to capitalists after legit production costs are covered (call that money potential profits, or surplus value in Marx). Capitalists "maintaining a good life-style" is just one use for potential profits. The surplus is actually divided many ways (e.g., it covers all government budgets) and what shows up as "profits" is the result of the interaction of many factors that constantly change.
In any case, there is a contradiction between the drive of capital to expand and the desire of individuals to capture more of the surplus for themselves. Lately, as globalization has heightened the competition between capitals, capitalists have responded by restricting labor's share, and they have tried to expand the surplus available to them by means of financial manipulations that have produced what seems to be an ever expanding financial bubble. The contradictions do seems to be getting sharper.