Most commonly, mission agencies treat their missionaries as Form W-2 employees (and, I believe, properly do so). They classify disbursements to them in categories such as cash compensation, housing allowance, and reimbursable employee business expenses.
The question has been asked, "Are there any IRS restrictions to consider in a mission agency's policy for the quantity of trips back to the home country? Because long-term missionaries are employees and eligible for accountable expense reimbursement arrangements, a common practice is to classify travel costs for furlough leave as reimbursable business expenses."
This question is addressed by IRS Publication 463. The Publication asks the question, "What Travel Expenses Are Deductible?" then answers it:
"Once you have determined that you are traveling away from your tax home [the foreign mission location, in most cases], you can determine what travel expenses are deductible. You can deduct ordinary and necessary expenses you have when you travel away from home on business. The type of expense you can deduct depends on the facts and your circumstances.
"If a spouse, dependent, or other individual goes with you on a business trip, you generally cannot deduct his or her travel expenses. You can deduct the travel expenses of someone who goes with you if that person: (1) is your employee, (2) has a bona fide business purpose for the travel, and (3) would otherwise be allowed to deduct the travel expenses.
"If a business associate travels with you and meets the conditions in (2) and (3) above, you can deduct the travel expenses you have for that person. A business associate is someone with whom you could reasonably expect to actively conduct business. A business associate can be a current or prospective (likely to become) customer, client, supplier, employee, agent, partner, or professional advisor. A bona fide business purpose exists if you can prove a real business purpose for the individual's presence. Incidental services, such as typing notes or assisting in entertaining customers, are not enough to make the expenses deductible."
In the case of a missionary family, my experience is that both spouses are expected to represent the ministry of the family. Whether the children's presence is "ordinary and necessary" (using the IRS definition) must be determined based on the facts and circumstances of the situation.
There is no maximum number of trips that the IRS will permit. Rather, deductibility is determined based on the above criteria. A missionary returning to the US simply to "drop off" his college student at school seems to fall short of the criteria. At the opposite extreme, doing so during an extended furlough of reporting to churches should only deny deductibility for the excess expenses incurred related to the personal nature of the college trip (i.e., extra mileage, meals and lodging will not be deductible).