A 45-year-old can have a absolutely have a healthy pregnancy. Much depends on the mom's medical and physical condition before pregnancy -- a healthy, fit 45-year-old will likely do better than an unhealthy, overweight 20-year-old smoker.
Of course, there are risks to both mom and baby as mom gets older. Foremost is the increase in genetic defects such as Down syndrome. As a woman and her eggs age, it is more likely that the egg will be damaged. The risk of bearing a baby with Down syndrome in a 20-year-old is one in 1,400; in a 30-year-old, it's one in 900; in a 40-year-old, one in 100; and in a 45-year-old, one in 25. Down syndrome and many other chromosomal abnormalities may be detected before birth by either chorionic villus sampling or amniocentesis. The risk of an early miscarriage is higher in older women as well, and this is directly related to that increased chance of a chromosomal defect.
Older women also are more likely to have preexisting medical problems, such as diabetes and high blood pressure. If either of these is already present, pregnancy may worsen them. Appropriate management will maximize the chances of delivering a healthy baby and minimize any adverse impact on the woman. Also, the chance of developing either high blood pressure or diabetes for the first time during a pregnancy is higher in women over age 35; again, with good prenatal care, these conditions can be detected and treated without significant consequences to either mom or baby.